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Simplifying 4 = -15x2 + 120x Reorder the terms: 4 = 120x + -15x2 Solving 4 = 120x + -15x2 Solving for variable 'x'. Reorder the terms: 4 + -120x + 15x2 = 120x + -120x + -15x2 + 15x2 Combine like terms: 120x + -120x = 0 4 + -120x + 15x2 = 0 + -15x2 + 15x2 4 + -120x + 15x2 = -15x2 + 15x2 Combine like terms: -15x2 + 15x2 = 0 4 + -120x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.2666666667 + -8x + x2 = 0 Move the constant term to the right: Add '-0.2666666667' to each side of the equation. 0.2666666667 + -8x + -0.2666666667 + x2 = 0 + -0.2666666667 Reorder the terms: 0.2666666667 + -0.2666666667 + -8x + x2 = 0 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + -8x + x2 = 0 + -0.2666666667 -8x + x2 = 0 + -0.2666666667 Combine like terms: 0 + -0.2666666667 = -0.2666666667 -8x + x2 = -0.2666666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -0.2666666667 + 16 Reorder the terms: 16 + -8x + x2 = -0.2666666667 + 16 Combine like terms: -0.2666666667 + 16 = 15.7333333333 16 + -8x + x2 = 15.7333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.7333333333 Calculate the square root of the right side: 3.966526608 Break this problem into two subproblems by setting (x + -4) equal to 3.966526608 and -3.966526608.Subproblem 1
x + -4 = 3.966526608 Simplifying x + -4 = 3.966526608 Reorder the terms: -4 + x = 3.966526608 Solving -4 + x = 3.966526608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.966526608 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.966526608 + 4 x = 3.966526608 + 4 Combine like terms: 3.966526608 + 4 = 7.966526608 x = 7.966526608 Simplifying x = 7.966526608Subproblem 2
x + -4 = -3.966526608 Simplifying x + -4 = -3.966526608 Reorder the terms: -4 + x = -3.966526608 Solving -4 + x = -3.966526608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.966526608 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.966526608 + 4 x = -3.966526608 + 4 Combine like terms: -3.966526608 + 4 = 0.033473392 x = 0.033473392 Simplifying x = 0.033473392Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.966526608, 0.033473392}
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