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Simplifying 16x2 + 150x + 5 = 7 Reorder the terms: 5 + 150x + 16x2 = 7 Solving 5 + 150x + 16x2 = 7 Solving for variable 'x'. Reorder the terms: 5 + -7 + 150x + 16x2 = 7 + -7 Combine like terms: 5 + -7 = -2 -2 + 150x + 16x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -2 + 150x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 75x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 75x + 8x2)' equal to zero and attempt to solve: Simplifying -1 + 75x + 8x2 = 0 Solving -1 + 75x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + 9.375x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 9.375x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 9.375x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 9.375x + x2 = 0 + 0.125 9.375x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 9.375x + x2 = 0.125 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 = 0.125 + 21.97265625 Reorder the terms: 21.97265625 + 9.375x + x2 = 0.125 + 21.97265625 Combine like terms: 0.125 + 21.97265625 = 22.09765625 21.97265625 + 9.375x + x2 = 22.09765625 Factor a perfect square on the left side: (x + 4.6875)(x + 4.6875) = 22.09765625 Calculate the square root of the right side: 4.700814424 Break this problem into two subproblems by setting (x + 4.6875) equal to 4.700814424 and -4.700814424.Subproblem 1
x + 4.6875 = 4.700814424 Simplifying x + 4.6875 = 4.700814424 Reorder the terms: 4.6875 + x = 4.700814424 Solving 4.6875 + x = 4.700814424 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 = 4.700814424 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = 4.700814424 + -4.6875 x = 4.700814424 + -4.6875 Combine like terms: 4.700814424 + -4.6875 = 0.013314424 x = 0.013314424 Simplifying x = 0.013314424Subproblem 2
x + 4.6875 = -4.700814424 Simplifying x + 4.6875 = -4.700814424 Reorder the terms: 4.6875 + x = -4.700814424 Solving 4.6875 + x = -4.700814424 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 = -4.700814424 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = -4.700814424 + -4.6875 x = -4.700814424 + -4.6875 Combine like terms: -4.700814424 + -4.6875 = -9.388314424 x = -9.388314424 Simplifying x = -9.388314424Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.013314424, -9.388314424}Solution
x = {0.013314424, -9.388314424}
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