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Simplifying 0 = -16x2 + 150x + -3 Reorder the terms: 0 = -3 + 150x + -16x2 Solving 0 = -3 + 150x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 3 = 3 3 + -150x + 16x2 = -3 + 150x + -16x2 + 3 + -150x + 16x2 Reorder the terms: 3 + -150x + 16x2 = -3 + 3 + 150x + -150x + -16x2 + 16x2 Combine like terms: -3 + 3 = 0 3 + -150x + 16x2 = 0 + 150x + -150x + -16x2 + 16x2 3 + -150x + 16x2 = 150x + -150x + -16x2 + 16x2 Combine like terms: 150x + -150x = 0 3 + -150x + 16x2 = 0 + -16x2 + 16x2 3 + -150x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 3 + -150x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1875 + -9.375x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -9.375x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -9.375x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -9.375x + x2 = 0 + -0.1875 -9.375x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -9.375x + x2 = -0.1875 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 = -0.1875 + 21.97265625 Reorder the terms: 21.97265625 + -9.375x + x2 = -0.1875 + 21.97265625 Combine like terms: -0.1875 + 21.97265625 = 21.78515625 21.97265625 + -9.375x + x2 = 21.78515625 Factor a perfect square on the left side: (x + -4.6875)(x + -4.6875) = 21.78515625 Calculate the square root of the right side: 4.66745715 Break this problem into two subproblems by setting (x + -4.6875) equal to 4.66745715 and -4.66745715.Subproblem 1
x + -4.6875 = 4.66745715 Simplifying x + -4.6875 = 4.66745715 Reorder the terms: -4.6875 + x = 4.66745715 Solving -4.6875 + x = 4.66745715 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 = 4.66745715 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = 4.66745715 + 4.6875 x = 4.66745715 + 4.6875 Combine like terms: 4.66745715 + 4.6875 = 9.35495715 x = 9.35495715 Simplifying x = 9.35495715Subproblem 2
x + -4.6875 = -4.66745715 Simplifying x + -4.6875 = -4.66745715 Reorder the terms: -4.6875 + x = -4.66745715 Solving -4.6875 + x = -4.66745715 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 = -4.66745715 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = -4.66745715 + 4.6875 x = -4.66745715 + 4.6875 Combine like terms: -4.66745715 + 4.6875 = 0.02004285 x = 0.02004285 Simplifying x = 0.02004285Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.35495715, 0.02004285}
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