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Simplifying 2(x + 1.3) * 4(5 + -1x) = 15 Reorder the terms: 2(1.3 + x) * 4(5 + -1x) = 15 Reorder the terms for easier multiplication: 2 * 4(1.3 + x)(5 + -1x) = 15 Multiply 2 * 4 8(1.3 + x)(5 + -1x) = 15 Multiply (1.3 + x) * (5 + -1x) 8(1.3(5 + -1x) + x(5 + -1x)) = 15 8((5 * 1.3 + -1x * 1.3) + x(5 + -1x)) = 15 8((6.5 + -1.3x) + x(5 + -1x)) = 15 8(6.5 + -1.3x + (5 * x + -1x * x)) = 15 8(6.5 + -1.3x + (5x + -1x2)) = 15 Combine like terms: -1.3x + 5x = 3.7x 8(6.5 + 3.7x + -1x2) = 15 (6.5 * 8 + 3.7x * 8 + -1x2 * 8) = 15 (52 + 29.6x + -8x2) = 15 Solving 52 + 29.6x + -8x2 = 15 Solving for variable 'x'. Reorder the terms: 52 + -15 + 29.6x + -8x2 = 15 + -15 Combine like terms: 52 + -15 = 37 37 + 29.6x + -8x2 = 15 + -15 Combine like terms: 15 + -15 = 0 37 + 29.6x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.625 + -3.7x + x2 = 0 Move the constant term to the right: Add '4.625' to each side of the equation. -4.625 + -3.7x + 4.625 + x2 = 0 + 4.625 Reorder the terms: -4.625 + 4.625 + -3.7x + x2 = 0 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + -3.7x + x2 = 0 + 4.625 -3.7x + x2 = 0 + 4.625 Combine like terms: 0 + 4.625 = 4.625 -3.7x + x2 = 4.625 The x term is -3.7x. Take half its coefficient (-1.85). Square it (3.4225) and add it to both sides. Add '3.4225' to each side of the equation. -3.7x + 3.4225 + x2 = 4.625 + 3.4225 Reorder the terms: 3.4225 + -3.7x + x2 = 4.625 + 3.4225 Combine like terms: 4.625 + 3.4225 = 8.0475 3.4225 + -3.7x + x2 = 8.0475 Factor a perfect square on the left side: (x + -1.85)(x + -1.85) = 8.0475 Calculate the square root of the right side: 2.836811591 Break this problem into two subproblems by setting (x + -1.85) equal to 2.836811591 and -2.836811591.Subproblem 1
x + -1.85 = 2.836811591 Simplifying x + -1.85 = 2.836811591 Reorder the terms: -1.85 + x = 2.836811591 Solving -1.85 + x = 2.836811591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.85' to each side of the equation. -1.85 + 1.85 + x = 2.836811591 + 1.85 Combine like terms: -1.85 + 1.85 = 0.00 0.00 + x = 2.836811591 + 1.85 x = 2.836811591 + 1.85 Combine like terms: 2.836811591 + 1.85 = 4.686811591 x = 4.686811591 Simplifying x = 4.686811591Subproblem 2
x + -1.85 = -2.836811591 Simplifying x + -1.85 = -2.836811591 Reorder the terms: -1.85 + x = -2.836811591 Solving -1.85 + x = -2.836811591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.85' to each side of the equation. -1.85 + 1.85 + x = -2.836811591 + 1.85 Combine like terms: -1.85 + 1.85 = 0.00 0.00 + x = -2.836811591 + 1.85 x = -2.836811591 + 1.85 Combine like terms: -2.836811591 + 1.85 = -0.986811591 x = -0.986811591 Simplifying x = -0.986811591Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.686811591, -0.986811591}
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