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Simplifying -16x2 + 350x + 40 = 500 Reorder the terms: 40 + 350x + -16x2 = 500 Solving 40 + 350x + -16x2 = 500 Solving for variable 'x'. Reorder the terms: 40 + -500 + 350x + -16x2 = 500 + -500 Combine like terms: 40 + -500 = -460 -460 + 350x + -16x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -460 + 350x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-230 + 175x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-230 + 175x + -8x2)' equal to zero and attempt to solve: Simplifying -230 + 175x + -8x2 = 0 Solving -230 + 175x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 28.75 + -21.875x + x2 = 0 Move the constant term to the right: Add '-28.75' to each side of the equation. 28.75 + -21.875x + -28.75 + x2 = 0 + -28.75 Reorder the terms: 28.75 + -28.75 + -21.875x + x2 = 0 + -28.75 Combine like terms: 28.75 + -28.75 = 0.00 0.00 + -21.875x + x2 = 0 + -28.75 -21.875x + x2 = 0 + -28.75 Combine like terms: 0 + -28.75 = -28.75 -21.875x + x2 = -28.75 The x term is -21.875x. Take half its coefficient (-10.9375). Square it (119.6289063) and add it to both sides. Add '119.6289063' to each side of the equation. -21.875x + 119.6289063 + x2 = -28.75 + 119.6289063 Reorder the terms: 119.6289063 + -21.875x + x2 = -28.75 + 119.6289063 Combine like terms: -28.75 + 119.6289063 = 90.8789063 119.6289063 + -21.875x + x2 = 90.8789063 Factor a perfect square on the left side: (x + -10.9375)(x + -10.9375) = 90.8789063 Calculate the square root of the right side: 9.533042867 Break this problem into two subproblems by setting (x + -10.9375) equal to 9.533042867 and -9.533042867.Subproblem 1
x + -10.9375 = 9.533042867 Simplifying x + -10.9375 = 9.533042867 Reorder the terms: -10.9375 + x = 9.533042867 Solving -10.9375 + x = 9.533042867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.9375' to each side of the equation. -10.9375 + 10.9375 + x = 9.533042867 + 10.9375 Combine like terms: -10.9375 + 10.9375 = 0.0000 0.0000 + x = 9.533042867 + 10.9375 x = 9.533042867 + 10.9375 Combine like terms: 9.533042867 + 10.9375 = 20.470542867 x = 20.470542867 Simplifying x = 20.470542867Subproblem 2
x + -10.9375 = -9.533042867 Simplifying x + -10.9375 = -9.533042867 Reorder the terms: -10.9375 + x = -9.533042867 Solving -10.9375 + x = -9.533042867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.9375' to each side of the equation. -10.9375 + 10.9375 + x = -9.533042867 + 10.9375 Combine like terms: -10.9375 + 10.9375 = 0.0000 0.0000 + x = -9.533042867 + 10.9375 x = -9.533042867 + 10.9375 Combine like terms: -9.533042867 + 10.9375 = 1.404457133 x = 1.404457133 Simplifying x = 1.404457133Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.470542867, 1.404457133}Solution
x = {20.470542867, 1.404457133}
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