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Simplifying 42 + -3(x + -11) * x = 3 Reorder the terms: 42 + -3(-11 + x) * x = 3 Reorder the terms for easier multiplication: 42 + -3x(-11 + x) = 3 42 + (-11 * -3x + x * -3x) = 3 42 + (33x + -3x2) = 3 Solving 42 + 33x + -3x2 = 3 Solving for variable 'x'. Reorder the terms: 42 + -3 + 33x + -3x2 = 3 + -3 Combine like terms: 42 + -3 = 39 39 + 33x + -3x2 = 3 + -3 Combine like terms: 3 + -3 = 0 39 + 33x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(13 + 11x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(13 + 11x + -1x2)' equal to zero and attempt to solve: Simplifying 13 + 11x + -1x2 = 0 Solving 13 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -11x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -11x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -11x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -11x + x2 = 0 + 13 -11x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -11x + x2 = 13 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 = 13 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 13 + 30.25 Combine like terms: 13 + 30.25 = 43.25 30.25 + -11x + x2 = 43.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + -5.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + -5.5 = 6.576473219 Simplifying x + -5.5 = 6.576473219 Reorder the terms: -5.5 + x = 6.576473219 Solving -5.5 + x = 6.576473219 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 = 6.576473219 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.576473219 + 5.5 x = 6.576473219 + 5.5 Combine like terms: 6.576473219 + 5.5 = 12.076473219 x = 12.076473219 Simplifying x = 12.076473219Subproblem 2
x + -5.5 = -6.576473219 Simplifying x + -5.5 = -6.576473219 Reorder the terms: -5.5 + x = -6.576473219 Solving -5.5 + x = -6.576473219 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 = -6.576473219 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.576473219 + 5.5 x = -6.576473219 + 5.5 Combine like terms: -6.576473219 + 5.5 = -1.076473219 x = -1.076473219 Simplifying x = -1.076473219Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.076473219, -1.076473219}Solution
x = {12.076473219, -1.076473219}
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