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Simplifying 5 + -1(8x + -7) * 18x = 31x + -1(90 + 28x) + -45 Reorder the terms: 5 + -1(-7 + 8x) * 18x = 31x + -1(90 + 28x) + -45 Reorder the terms for easier multiplication: 5 + -1 * 18x(-7 + 8x) = 31x + -1(90 + 28x) + -45 Multiply -1 * 18 5 + -18x(-7 + 8x) = 31x + -1(90 + 28x) + -45 5 + (-7 * -18x + 8x * -18x) = 31x + -1(90 + 28x) + -45 5 + (126x + -144x2) = 31x + -1(90 + 28x) + -45 5 + 126x + -144x2 = 31x + (90 * -1 + 28x * -1) + -45 5 + 126x + -144x2 = 31x + (-90 + -28x) + -45 Reorder the terms: 5 + 126x + -144x2 = -90 + -45 + 31x + -28x Combine like terms: -90 + -45 = -135 5 + 126x + -144x2 = -135 + 31x + -28x Combine like terms: 31x + -28x = 3x 5 + 126x + -144x2 = -135 + 3x Solving 5 + 126x + -144x2 = -135 + 3x Solving for variable 'x'. Reorder the terms: 5 + 135 + 126x + -3x + -144x2 = -135 + 3x + 135 + -3x Combine like terms: 5 + 135 = 140 140 + 126x + -3x + -144x2 = -135 + 3x + 135 + -3x Combine like terms: 126x + -3x = 123x 140 + 123x + -144x2 = -135 + 3x + 135 + -3x Reorder the terms: 140 + 123x + -144x2 = -135 + 135 + 3x + -3x Combine like terms: -135 + 135 = 0 140 + 123x + -144x2 = 0 + 3x + -3x 140 + 123x + -144x2 = 3x + -3x Combine like terms: 3x + -3x = 0 140 + 123x + -144x2 = 0 Begin completing the square. Divide all terms by -144 the coefficient of the squared term: Divide each side by '-144'. -0.9722222222 + -0.8541666667x + x2 = 0 Move the constant term to the right: Add '0.9722222222' to each side of the equation. -0.9722222222 + -0.8541666667x + 0.9722222222 + x2 = 0 + 0.9722222222 Reorder the terms: -0.9722222222 + 0.9722222222 + -0.8541666667x + x2 = 0 + 0.9722222222 Combine like terms: -0.9722222222 + 0.9722222222 = 0.0000000000 0.0000000000 + -0.8541666667x + x2 = 0 + 0.9722222222 -0.8541666667x + x2 = 0 + 0.9722222222 Combine like terms: 0 + 0.9722222222 = 0.9722222222 -0.8541666667x + x2 = 0.9722222222 The x term is -0.8541666667x. Take half its coefficient (-0.4270833334). Square it (0.1824001737) and add it to both sides. Add '0.1824001737' to each side of the equation. -0.8541666667x + 0.1824001737 + x2 = 0.9722222222 + 0.1824001737 Reorder the terms: 0.1824001737 + -0.8541666667x + x2 = 0.9722222222 + 0.1824001737 Combine like terms: 0.9722222222 + 0.1824001737 = 1.1546223959 0.1824001737 + -0.8541666667x + x2 = 1.1546223959 Factor a perfect square on the left side: (x + -0.4270833334)(x + -0.4270833334) = 1.1546223959 Calculate the square root of the right side: 1.074533571 Break this problem into two subproblems by setting (x + -0.4270833334) equal to 1.074533571 and -1.074533571.Subproblem 1
x + -0.4270833334 = 1.074533571 Simplifying x + -0.4270833334 = 1.074533571 Reorder the terms: -0.4270833334 + x = 1.074533571 Solving -0.4270833334 + x = 1.074533571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4270833334' to each side of the equation. -0.4270833334 + 0.4270833334 + x = 1.074533571 + 0.4270833334 Combine like terms: -0.4270833334 + 0.4270833334 = 0.0000000000 0.0000000000 + x = 1.074533571 + 0.4270833334 x = 1.074533571 + 0.4270833334 Combine like terms: 1.074533571 + 0.4270833334 = 1.5016169044 x = 1.5016169044 Simplifying x = 1.5016169044Subproblem 2
x + -0.4270833334 = -1.074533571 Simplifying x + -0.4270833334 = -1.074533571 Reorder the terms: -0.4270833334 + x = -1.074533571 Solving -0.4270833334 + x = -1.074533571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4270833334' to each side of the equation. -0.4270833334 + 0.4270833334 + x = -1.074533571 + 0.4270833334 Combine like terms: -0.4270833334 + 0.4270833334 = 0.0000000000 0.0000000000 + x = -1.074533571 + 0.4270833334 x = -1.074533571 + 0.4270833334 Combine like terms: -1.074533571 + 0.4270833334 = -0.6474502376 x = -0.6474502376 Simplifying x = -0.6474502376Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5016169044, -0.6474502376}
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