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Simplifying -16x2 + 150x = 40 Reorder the terms: 150x + -16x2 = 40 Solving 150x + -16x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + 150x + -16x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 150x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 75x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + 75x + -8x2)' equal to zero and attempt to solve: Simplifying -20 + 75x + -8x2 = 0 Solving -20 + 75x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 2.5 + -9.375x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -9.375x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -9.375x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -9.375x + x2 = 0 + -2.5 -9.375x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -9.375x + x2 = -2.5 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 = -2.5 + 21.97265625 Reorder the terms: 21.97265625 + -9.375x + x2 = -2.5 + 21.97265625 Combine like terms: -2.5 + 21.97265625 = 19.47265625 21.97265625 + -9.375x + x2 = 19.47265625 Factor a perfect square on the left side: (x + -4.6875)(x + -4.6875) = 19.47265625 Calculate the square root of the right side: 4.412783277 Break this problem into two subproblems by setting (x + -4.6875) equal to 4.412783277 and -4.412783277.Subproblem 1
x + -4.6875 = 4.412783277 Simplifying x + -4.6875 = 4.412783277 Reorder the terms: -4.6875 + x = 4.412783277 Solving -4.6875 + x = 4.412783277 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 = 4.412783277 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = 4.412783277 + 4.6875 x = 4.412783277 + 4.6875 Combine like terms: 4.412783277 + 4.6875 = 9.100283277 x = 9.100283277 Simplifying x = 9.100283277Subproblem 2
x + -4.6875 = -4.412783277 Simplifying x + -4.6875 = -4.412783277 Reorder the terms: -4.6875 + x = -4.412783277 Solving -4.6875 + x = -4.412783277 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 = -4.412783277 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = -4.412783277 + 4.6875 x = -4.412783277 + 4.6875 Combine like terms: -4.412783277 + 4.6875 = 0.274716723 x = 0.274716723 Simplifying x = 0.274716723Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.100283277, 0.274716723}Solution
x = {9.100283277, 0.274716723}
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