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Simplifying -12x(x + -12) = -9(1 + 7x) Reorder the terms: -12x(-12 + x) = -9(1 + 7x) (-12 * -12x + x * -12x) = -9(1 + 7x) (144x + -12x2) = -9(1 + 7x) 144x + -12x2 = (1 * -9 + 7x * -9) 144x + -12x2 = (-9 + -63x) Solving 144x + -12x2 = -9 + -63x Solving for variable 'x'. Reorder the terms: 9 + 144x + 63x + -12x2 = -9 + -63x + 9 + 63x Combine like terms: 144x + 63x = 207x 9 + 207x + -12x2 = -9 + -63x + 9 + 63x Reorder the terms: 9 + 207x + -12x2 = -9 + 9 + -63x + 63x Combine like terms: -9 + 9 = 0 9 + 207x + -12x2 = 0 + -63x + 63x 9 + 207x + -12x2 = -63x + 63x Combine like terms: -63x + 63x = 0 9 + 207x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 69x + -4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 69x + -4x2)' equal to zero and attempt to solve: Simplifying 3 + 69x + -4x2 = 0 Solving 3 + 69x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -17.25x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -17.25x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -17.25x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -17.25x + x2 = 0 + 0.75 -17.25x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -17.25x + x2 = 0.75 The x term is -17.25x. Take half its coefficient (-8.625). Square it (74.390625) and add it to both sides. Add '74.390625' to each side of the equation. -17.25x + 74.390625 + x2 = 0.75 + 74.390625 Reorder the terms: 74.390625 + -17.25x + x2 = 0.75 + 74.390625 Combine like terms: 0.75 + 74.390625 = 75.140625 74.390625 + -17.25x + x2 = 75.140625 Factor a perfect square on the left side: (x + -8.625)(x + -8.625) = 75.140625 Calculate the square root of the right side: 8.668369224 Break this problem into two subproblems by setting (x + -8.625) equal to 8.668369224 and -8.668369224.Subproblem 1
x + -8.625 = 8.668369224 Simplifying x + -8.625 = 8.668369224 Reorder the terms: -8.625 + x = 8.668369224 Solving -8.625 + x = 8.668369224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.625' to each side of the equation. -8.625 + 8.625 + x = 8.668369224 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + x = 8.668369224 + 8.625 x = 8.668369224 + 8.625 Combine like terms: 8.668369224 + 8.625 = 17.293369224 x = 17.293369224 Simplifying x = 17.293369224Subproblem 2
x + -8.625 = -8.668369224 Simplifying x + -8.625 = -8.668369224 Reorder the terms: -8.625 + x = -8.668369224 Solving -8.625 + x = -8.668369224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.625' to each side of the equation. -8.625 + 8.625 + x = -8.668369224 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + x = -8.668369224 + 8.625 x = -8.668369224 + 8.625 Combine like terms: -8.668369224 + 8.625 = -0.043369224 x = -0.043369224 Simplifying x = -0.043369224Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.293369224, -0.043369224}Solution
x = {17.293369224, -0.043369224}
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