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Simplifying 7.5x2 + -63x + -492 = 0 Reorder the terms: -492 + -63x + 7.5x2 = 0 Solving -492 + -63x + 7.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.5 the coefficient of the squared term: Divide each side by '7.5'. -65.6 + -8.4x + x2 = 0 Move the constant term to the right: Add '65.6' to each side of the equation. -65.6 + -8.4x + 65.6 + x2 = 0 + 65.6 Reorder the terms: -65.6 + 65.6 + -8.4x + x2 = 0 + 65.6 Combine like terms: -65.6 + 65.6 = 0.0 0.0 + -8.4x + x2 = 0 + 65.6 -8.4x + x2 = 0 + 65.6 Combine like terms: 0 + 65.6 = 65.6 -8.4x + x2 = 65.6 The x term is -8.4x. Take half its coefficient (-4.2). Square it (17.64) and add it to both sides. Add '17.64' to each side of the equation. -8.4x + 17.64 + x2 = 65.6 + 17.64 Reorder the terms: 17.64 + -8.4x + x2 = 65.6 + 17.64 Combine like terms: 65.6 + 17.64 = 83.24 17.64 + -8.4x + x2 = 83.24 Factor a perfect square on the left side: (x + -4.2)(x + -4.2) = 83.24 Calculate the square root of the right side: 9.123595782 Break this problem into two subproblems by setting (x + -4.2) equal to 9.123595782 and -9.123595782.Subproblem 1
x + -4.2 = 9.123595782 Simplifying x + -4.2 = 9.123595782 Reorder the terms: -4.2 + x = 9.123595782 Solving -4.2 + x = 9.123595782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.2' to each side of the equation. -4.2 + 4.2 + x = 9.123595782 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = 9.123595782 + 4.2 x = 9.123595782 + 4.2 Combine like terms: 9.123595782 + 4.2 = 13.323595782 x = 13.323595782 Simplifying x = 13.323595782Subproblem 2
x + -4.2 = -9.123595782 Simplifying x + -4.2 = -9.123595782 Reorder the terms: -4.2 + x = -9.123595782 Solving -4.2 + x = -9.123595782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.2' to each side of the equation. -4.2 + 4.2 + x = -9.123595782 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = -9.123595782 + 4.2 x = -9.123595782 + 4.2 Combine like terms: -9.123595782 + 4.2 = -4.923595782 x = -4.923595782 Simplifying x = -4.923595782Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.323595782, -4.923595782}
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