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Simplifying 6x2 + 15x + -36 = x Reorder the terms: -36 + 15x + 6x2 = x Solving -36 + 15x + 6x2 = x Solving for variable 'x'. Reorder the terms: -36 + 15x + -1x + 6x2 = x + -1x Combine like terms: 15x + -1x = 14x -36 + 14x + 6x2 = x + -1x Combine like terms: x + -1x = 0 -36 + 14x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 7x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 7x + 3x2)' equal to zero and attempt to solve: Simplifying -18 + 7x + 3x2 = 0 Solving -18 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 2.333333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 2.333333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2.333333333x + x2 = 0 + 6 2.333333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 2.333333333x + x2 = 6 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 6 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 6 + 1.361111112 Combine like terms: 6 + 1.361111112 = 7.361111112 1.361111112 + 2.333333333x + x2 = 7.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 7.361111112 Calculate the square root of the right side: 2.713136766 Break this problem into two subproblems by setting (x + 1.166666667) equal to 2.713136766 and -2.713136766.Subproblem 1
x + 1.166666667 = 2.713136766 Simplifying x + 1.166666667 = 2.713136766 Reorder the terms: 1.166666667 + x = 2.713136766 Solving 1.166666667 + x = 2.713136766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 2.713136766 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 2.713136766 + -1.166666667 x = 2.713136766 + -1.166666667 Combine like terms: 2.713136766 + -1.166666667 = 1.546470099 x = 1.546470099 Simplifying x = 1.546470099Subproblem 2
x + 1.166666667 = -2.713136766 Simplifying x + 1.166666667 = -2.713136766 Reorder the terms: 1.166666667 + x = -2.713136766 Solving 1.166666667 + x = -2.713136766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -2.713136766 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -2.713136766 + -1.166666667 x = -2.713136766 + -1.166666667 Combine like terms: -2.713136766 + -1.166666667 = -3.879803433 x = -3.879803433 Simplifying x = -3.879803433Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.546470099, -3.879803433}Solution
x = {1.546470099, -3.879803433}
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