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Simplifying 42x = 9x2 + -36 Reorder the terms: 42x = -36 + 9x2 Solving 42x = -36 + 9x2 Solving for variable 'x'. Reorder the terms: 36 + 42x + -9x2 = -36 + 9x2 + 36 + -9x2 Reorder the terms: 36 + 42x + -9x2 = -36 + 36 + 9x2 + -9x2 Combine like terms: -36 + 36 = 0 36 + 42x + -9x2 = 0 + 9x2 + -9x2 36 + 42x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 36 + 42x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(12 + 14x + -3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(12 + 14x + -3x2)' equal to zero and attempt to solve: Simplifying 12 + 14x + -3x2 = 0 Solving 12 + 14x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4.666666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -4.666666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4.666666667x + x2 = 0 + 4 -4.666666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4.666666667x + x2 = 4 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 4 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 4 + 5.444444448 Combine like terms: 4 + 5.444444448 = 9.444444448 5.444444448 + -4.666666667x + x2 = 9.444444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 9.444444448 Calculate the square root of the right side: 3.073181486 Break this problem into two subproblems by setting (x + -2.333333334) equal to 3.073181486 and -3.073181486.Subproblem 1
x + -2.333333334 = 3.073181486 Simplifying x + -2.333333334 = 3.073181486 Reorder the terms: -2.333333334 + x = 3.073181486 Solving -2.333333334 + x = 3.073181486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 3.073181486 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 3.073181486 + 2.333333334 x = 3.073181486 + 2.333333334 Combine like terms: 3.073181486 + 2.333333334 = 5.40651482 x = 5.40651482 Simplifying x = 5.40651482Subproblem 2
x + -2.333333334 = -3.073181486 Simplifying x + -2.333333334 = -3.073181486 Reorder the terms: -2.333333334 + x = -3.073181486 Solving -2.333333334 + x = -3.073181486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -3.073181486 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -3.073181486 + 2.333333334 x = -3.073181486 + 2.333333334 Combine like terms: -3.073181486 + 2.333333334 = -0.739848152 x = -0.739848152 Simplifying x = -0.739848152Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.40651482, -0.739848152}Solution
x = {5.40651482, -0.739848152}
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