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Simplifying -5x(x + 11) + 542 = 23 + 24 Reorder the terms: -5x(11 + x) + 542 = 23 + 24 (11 * -5x + x * -5x) + 542 = 23 + 24 (-55x + -5x2) + 542 = 23 + 24 Reorder the terms: 542 + -55x + -5x2 = 23 + 24 Combine like terms: 23 + 24 = 47 542 + -55x + -5x2 = 47 Solving 542 + -55x + -5x2 = 47 Solving for variable 'x'. Reorder the terms: 542 + -47 + -55x + -5x2 = 47 + -47 Combine like terms: 542 + -47 = 495 495 + -55x + -5x2 = 47 + -47 Combine like terms: 47 + -47 = 0 495 + -55x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(99 + -11x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(99 + -11x + -1x2)' equal to zero and attempt to solve: Simplifying 99 + -11x + -1x2 = 0 Solving 99 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -99 + 11x + x2 = 0 Move the constant term to the right: Add '99' to each side of the equation. -99 + 11x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 11x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 11x + x2 = 0 + 99 11x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 11x + x2 = 99 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 99 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 99 + 30.25 Combine like terms: 99 + 30.25 = 129.25 30.25 + 11x + x2 = 129.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 129.25 Calculate the square root of the right side: 11.368817001 Break this problem into two subproblems by setting (x + 5.5) equal to 11.368817001 and -11.368817001.Subproblem 1
x + 5.5 = 11.368817001 Simplifying x + 5.5 = 11.368817001 Reorder the terms: 5.5 + x = 11.368817001 Solving 5.5 + x = 11.368817001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 11.368817001 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 11.368817001 + -5.5 x = 11.368817001 + -5.5 Combine like terms: 11.368817001 + -5.5 = 5.868817001 x = 5.868817001 Simplifying x = 5.868817001Subproblem 2
x + 5.5 = -11.368817001 Simplifying x + 5.5 = -11.368817001 Reorder the terms: 5.5 + x = -11.368817001 Solving 5.5 + x = -11.368817001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -11.368817001 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -11.368817001 + -5.5 x = -11.368817001 + -5.5 Combine like terms: -11.368817001 + -5.5 = -16.868817001 x = -16.868817001 Simplifying x = -16.868817001Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.868817001, -16.868817001}Solution
x = {5.868817001, -16.868817001}
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