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Simplifying 36(x + -12)(x + -12) = 15 Reorder the terms: 36(-12 + x)(x + -12) = 15 Reorder the terms: 36(-12 + x)(-12 + x) = 15 Multiply (-12 + x) * (-12 + x) 36(-12(-12 + x) + x(-12 + x)) = 15 36((-12 * -12 + x * -12) + x(-12 + x)) = 15 36((144 + -12x) + x(-12 + x)) = 15 36(144 + -12x + (-12 * x + x * x)) = 15 36(144 + -12x + (-12x + x2)) = 15 Combine like terms: -12x + -12x = -24x 36(144 + -24x + x2) = 15 (144 * 36 + -24x * 36 + x2 * 36) = 15 (5184 + -864x + 36x2) = 15 Solving 5184 + -864x + 36x2 = 15 Solving for variable 'x'. Reorder the terms: 5184 + -15 + -864x + 36x2 = 15 + -15 Combine like terms: 5184 + -15 = 5169 5169 + -864x + 36x2 = 15 + -15 Combine like terms: 15 + -15 = 0 5169 + -864x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1723 + -288x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1723 + -288x + 12x2)' equal to zero and attempt to solve: Simplifying 1723 + -288x + 12x2 = 0 Solving 1723 + -288x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 143.5833333 + -24x + x2 = 0 Move the constant term to the right: Add '-143.5833333' to each side of the equation. 143.5833333 + -24x + -143.5833333 + x2 = 0 + -143.5833333 Reorder the terms: 143.5833333 + -143.5833333 + -24x + x2 = 0 + -143.5833333 Combine like terms: 143.5833333 + -143.5833333 = 0.0000000 0.0000000 + -24x + x2 = 0 + -143.5833333 -24x + x2 = 0 + -143.5833333 Combine like terms: 0 + -143.5833333 = -143.5833333 -24x + x2 = -143.5833333 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -143.5833333 + 144 Reorder the terms: 144 + -24x + x2 = -143.5833333 + 144 Combine like terms: -143.5833333 + 144 = 0.4166667 144 + -24x + x2 = 0.4166667 Factor a perfect square on the left side: (x + -12)(x + -12) = 0.4166667 Calculate the square root of the right side: 0.64549725 Break this problem into two subproblems by setting (x + -12) equal to 0.64549725 and -0.64549725.Subproblem 1
x + -12 = 0.64549725 Simplifying x + -12 = 0.64549725 Reorder the terms: -12 + x = 0.64549725 Solving -12 + x = 0.64549725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0.64549725 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0.64549725 + 12 x = 0.64549725 + 12 Combine like terms: 0.64549725 + 12 = 12.64549725 x = 12.64549725 Simplifying x = 12.64549725Subproblem 2
x + -12 = -0.64549725 Simplifying x + -12 = -0.64549725 Reorder the terms: -12 + x = -0.64549725 Solving -12 + x = -0.64549725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -0.64549725 + 12 Combine like terms: -12 + 12 = 0 0 + x = -0.64549725 + 12 x = -0.64549725 + 12 Combine like terms: -0.64549725 + 12 = 11.35450275 x = 11.35450275 Simplifying x = 11.35450275Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.64549725, 11.35450275}Solution
x = {12.64549725, 11.35450275}
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