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Simplifying 7 = -16x2 + 50x + 5 Reorder the terms: 7 = 5 + 50x + -16x2 Solving 7 = 5 + 50x + -16x2 Solving for variable 'x'. Combine like terms: 7 + -5 = 2 2 + -50x + 16x2 = 5 + 50x + -16x2 + -5 + -50x + 16x2 Reorder the terms: 2 + -50x + 16x2 = 5 + -5 + 50x + -50x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 2 + -50x + 16x2 = 0 + 50x + -50x + -16x2 + 16x2 2 + -50x + 16x2 = 50x + -50x + -16x2 + 16x2 Combine like terms: 50x + -50x = 0 2 + -50x + 16x2 = 0 + -16x2 + 16x2 2 + -50x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 2 + -50x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -25x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -25x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + -25x + 8x2 = 0 Solving 1 + -25x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -3.125x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -3.125x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -3.125x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -3.125x + x2 = 0 + -0.125 -3.125x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -3.125x + x2 = -0.125 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = -0.125 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = -0.125 + 2.44140625 Combine like terms: -0.125 + 2.44140625 = 2.31640625 2.44140625 + -3.125x + x2 = 2.31640625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 2.31640625 Calculate the square root of the right side: 1.521974458 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.521974458 and -1.521974458.Subproblem 1
x + -1.5625 = 1.521974458 Simplifying x + -1.5625 = 1.521974458 Reorder the terms: -1.5625 + x = 1.521974458 Solving -1.5625 + x = 1.521974458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.521974458 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.521974458 + 1.5625 x = 1.521974458 + 1.5625 Combine like terms: 1.521974458 + 1.5625 = 3.084474458 x = 3.084474458 Simplifying x = 3.084474458Subproblem 2
x + -1.5625 = -1.521974458 Simplifying x + -1.5625 = -1.521974458 Reorder the terms: -1.5625 + x = -1.521974458 Solving -1.5625 + x = -1.521974458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.521974458 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.521974458 + 1.5625 x = -1.521974458 + 1.5625 Combine like terms: -1.521974458 + 1.5625 = 0.040525542 x = 0.040525542 Simplifying x = 0.040525542Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.084474458, 0.040525542}Solution
x = {3.084474458, 0.040525542}
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