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Simplifying -4x + -2x(2x + 10) = -116 Reorder the terms: -4x + -2x(10 + 2x) = -116 -4x + (10 * -2x + 2x * -2x) = -116 -4x + (-20x + -4x2) = -116 Combine like terms: -4x + -20x = -24x -24x + -4x2 = -116 Solving -24x + -4x2 = -116 Solving for variable 'x'. Reorder the terms: 116 + -24x + -4x2 = -116 + 116 Combine like terms: -116 + 116 = 0 116 + -24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(29 + -6x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(29 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 29 + -6x + -1x2 = 0 Solving 29 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -29 + 6x + x2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + 6x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 6x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 6x + x2 = 0 + 29 6x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 6x + x2 = 29 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 29 + 9 Reorder the terms: 9 + 6x + x2 = 29 + 9 Combine like terms: 29 + 9 = 38 9 + 6x + x2 = 38 Factor a perfect square on the left side: (x + 3)(x + 3) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + 3) equal to 6.164414003 and -6.164414003.Subproblem 1
x + 3 = 6.164414003 Simplifying x + 3 = 6.164414003 Reorder the terms: 3 + x = 6.164414003 Solving 3 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.164414003 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.164414003 + -3 x = 6.164414003 + -3 Combine like terms: 6.164414003 + -3 = 3.164414003 x = 3.164414003 Simplifying x = 3.164414003Subproblem 2
x + 3 = -6.164414003 Simplifying x + 3 = -6.164414003 Reorder the terms: 3 + x = -6.164414003 Solving 3 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.164414003 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.164414003 + -3 x = -6.164414003 + -3 Combine like terms: -6.164414003 + -3 = -9.164414003 x = -9.164414003 Simplifying x = -9.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.164414003, -9.164414003}Solution
x = {3.164414003, -9.164414003}
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