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Simplifying 0 = 16x2 + 150x + 144 Reorder the terms: 0 = 144 + 150x + 16x2 Solving 0 = 144 + 150x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -144 = -144 -144 + -150x + -16x2 = 144 + 150x + 16x2 + -144 + -150x + -16x2 Reorder the terms: -144 + -150x + -16x2 = 144 + -144 + 150x + -150x + 16x2 + -16x2 Combine like terms: 144 + -144 = 0 -144 + -150x + -16x2 = 0 + 150x + -150x + 16x2 + -16x2 -144 + -150x + -16x2 = 150x + -150x + 16x2 + -16x2 Combine like terms: 150x + -150x = 0 -144 + -150x + -16x2 = 0 + 16x2 + -16x2 -144 + -150x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -144 + -150x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(72 + 75x + 8x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(72 + 75x + 8x2)' equal to zero and attempt to solve: Simplifying 72 + 75x + 8x2 = 0 Solving 72 + 75x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 9 + 9.375x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 9.375x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 9.375x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 9.375x + x2 = 0 + -9 9.375x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 9.375x + x2 = -9 The x term is 9.375x. Take half its coefficient (4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. 9.375x + 21.97265625 + x2 = -9 + 21.97265625 Reorder the terms: 21.97265625 + 9.375x + x2 = -9 + 21.97265625 Combine like terms: -9 + 21.97265625 = 12.97265625 21.97265625 + 9.375x + x2 = 12.97265625 Factor a perfect square on the left side: (x + 4.6875)(x + 4.6875) = 12.97265625 Calculate the square root of the right side: 3.601757384 Break this problem into two subproblems by setting (x + 4.6875) equal to 3.601757384 and -3.601757384.Subproblem 1
x + 4.6875 = 3.601757384 Simplifying x + 4.6875 = 3.601757384 Reorder the terms: 4.6875 + x = 3.601757384 Solving 4.6875 + x = 3.601757384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = 3.601757384 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = 3.601757384 + -4.6875 x = 3.601757384 + -4.6875 Combine like terms: 3.601757384 + -4.6875 = -1.085742616 x = -1.085742616 Simplifying x = -1.085742616Subproblem 2
x + 4.6875 = -3.601757384 Simplifying x + 4.6875 = -3.601757384 Reorder the terms: 4.6875 + x = -3.601757384 Solving 4.6875 + x = -3.601757384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = -3.601757384 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = -3.601757384 + -4.6875 x = -3.601757384 + -4.6875 Combine like terms: -3.601757384 + -4.6875 = -8.289257384 x = -8.289257384 Simplifying x = -8.289257384Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.085742616, -8.289257384}Solution
x = {-1.085742616, -8.289257384}
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