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Simplifying 18 + -1(x + 3) * 2x = 4 + (x + -5) Reorder the terms: 18 + -1(3 + x) * 2x = 4 + (x + -5) Reorder the terms for easier multiplication: 18 + -1 * 2x(3 + x) = 4 + (x + -5) Multiply -1 * 2 18 + -2x(3 + x) = 4 + (x + -5) 18 + (3 * -2x + x * -2x) = 4 + (x + -5) 18 + (-6x + -2x2) = 4 + (x + -5) Reorder the terms: 18 + -6x + -2x2 = 4 + (-5 + x) Remove parenthesis around (-5 + x) 18 + -6x + -2x2 = 4 + -5 + x Combine like terms: 4 + -5 = -1 18 + -6x + -2x2 = -1 + x Solving 18 + -6x + -2x2 = -1 + x Solving for variable 'x'. Reorder the terms: 18 + 1 + -6x + -1x + -2x2 = -1 + x + 1 + -1x Combine like terms: 18 + 1 = 19 19 + -6x + -1x + -2x2 = -1 + x + 1 + -1x Combine like terms: -6x + -1x = -7x 19 + -7x + -2x2 = -1 + x + 1 + -1x Reorder the terms: 19 + -7x + -2x2 = -1 + 1 + x + -1x Combine like terms: -1 + 1 = 0 19 + -7x + -2x2 = 0 + x + -1x 19 + -7x + -2x2 = x + -1x Combine like terms: x + -1x = 0 19 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -9.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 3.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 3.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 3.5x + x2 = 0 + 9.5 3.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 3.5x + x2 = 9.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 9.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 9.5 + 3.0625 Combine like terms: 9.5 + 3.0625 = 12.5625 3.0625 + 3.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 1.75) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 1.75 = 3.54436172 Simplifying x + 1.75 = 3.54436172 Reorder the terms: 1.75 + x = 3.54436172 Solving 1.75 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.54436172 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.54436172 + -1.75 x = 3.54436172 + -1.75 Combine like terms: 3.54436172 + -1.75 = 1.79436172 x = 1.79436172 Simplifying x = 1.79436172Subproblem 2
x + 1.75 = -3.54436172 Simplifying x + 1.75 = -3.54436172 Reorder the terms: 1.75 + x = -3.54436172 Solving 1.75 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.54436172 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.54436172 + -1.75 x = -3.54436172 + -1.75 Combine like terms: -3.54436172 + -1.75 = -5.29436172 x = -5.29436172 Simplifying x = -5.29436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.79436172, -5.29436172}
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