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Simplifying 8x2 + -30x = 135 Reorder the terms: -30x + 8x2 = 135 Solving -30x + 8x2 = 135 Solving for variable 'x'. Reorder the terms: -135 + -30x + 8x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + -30x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -16.875 + -3.75x + x2 = 0 Move the constant term to the right: Add '16.875' to each side of the equation. -16.875 + -3.75x + 16.875 + x2 = 0 + 16.875 Reorder the terms: -16.875 + 16.875 + -3.75x + x2 = 0 + 16.875 Combine like terms: -16.875 + 16.875 = 0.000 0.000 + -3.75x + x2 = 0 + 16.875 -3.75x + x2 = 0 + 16.875 Combine like terms: 0 + 16.875 = 16.875 -3.75x + x2 = 16.875 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 16.875 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 16.875 + 3.515625 Combine like terms: 16.875 + 3.515625 = 20.390625 3.515625 + -3.75x + x2 = 20.390625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 20.390625 Calculate the square root of the right side: 4.515597967 Break this problem into two subproblems by setting (x + -1.875) equal to 4.515597967 and -4.515597967.Subproblem 1
x + -1.875 = 4.515597967 Simplifying x + -1.875 = 4.515597967 Reorder the terms: -1.875 + x = 4.515597967 Solving -1.875 + x = 4.515597967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 4.515597967 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 4.515597967 + 1.875 x = 4.515597967 + 1.875 Combine like terms: 4.515597967 + 1.875 = 6.390597967 x = 6.390597967 Simplifying x = 6.390597967Subproblem 2
x + -1.875 = -4.515597967 Simplifying x + -1.875 = -4.515597967 Reorder the terms: -1.875 + x = -4.515597967 Solving -1.875 + x = -4.515597967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -4.515597967 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -4.515597967 + 1.875 x = -4.515597967 + 1.875 Combine like terms: -4.515597967 + 1.875 = -2.640597967 x = -2.640597967 Simplifying x = -2.640597967Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.390597967, -2.640597967}
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