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Simplifying 4x2 + -3x + 30 = 360 Reorder the terms: 30 + -3x + 4x2 = 360 Solving 30 + -3x + 4x2 = 360 Solving for variable 'x'. Reorder the terms: 30 + -360 + -3x + 4x2 = 360 + -360 Combine like terms: 30 + -360 = -330 -330 + -3x + 4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -330 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -82.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '82.5' to each side of the equation. -82.5 + -0.75x + 82.5 + x2 = 0 + 82.5 Reorder the terms: -82.5 + 82.5 + -0.75x + x2 = 0 + 82.5 Combine like terms: -82.5 + 82.5 = 0.0 0.0 + -0.75x + x2 = 0 + 82.5 -0.75x + x2 = 0 + 82.5 Combine like terms: 0 + 82.5 = 82.5 -0.75x + x2 = 82.5 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 82.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 82.5 + 0.140625 Combine like terms: 82.5 + 0.140625 = 82.640625 0.140625 + -0.75x + x2 = 82.640625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 82.640625 Calculate the square root of the right side: 9.090688918 Break this problem into two subproblems by setting (x + -0.375) equal to 9.090688918 and -9.090688918.Subproblem 1
x + -0.375 = 9.090688918 Simplifying x + -0.375 = 9.090688918 Reorder the terms: -0.375 + x = 9.090688918 Solving -0.375 + x = 9.090688918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 9.090688918 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 9.090688918 + 0.375 x = 9.090688918 + 0.375 Combine like terms: 9.090688918 + 0.375 = 9.465688918 x = 9.465688918 Simplifying x = 9.465688918Subproblem 2
x + -0.375 = -9.090688918 Simplifying x + -0.375 = -9.090688918 Reorder the terms: -0.375 + x = -9.090688918 Solving -0.375 + x = -9.090688918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -9.090688918 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -9.090688918 + 0.375 x = -9.090688918 + 0.375 Combine like terms: -9.090688918 + 0.375 = -8.715688918 x = -8.715688918 Simplifying x = -8.715688918Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.465688918, -8.715688918}
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