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Simplifying 4x2 + 9x = 292.5 Reorder the terms: 9x + 4x2 = 292.5 Solving 9x + 4x2 = 292.5 Solving for variable 'x'. Reorder the terms: -292.5 + 9x + 4x2 = 292.5 + -292.5 Combine like terms: 292.5 + -292.5 = 0.0 -292.5 + 9x + 4x2 = 0.0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -73.125 + 2.25x + x2 = 0.0 Move the constant term to the right: Add '73.125' to each side of the equation. -73.125 + 2.25x + 73.125 + x2 = 0.0 + 73.125 Reorder the terms: -73.125 + 73.125 + 2.25x + x2 = 0.0 + 73.125 Combine like terms: -73.125 + 73.125 = 0.000 0.000 + 2.25x + x2 = 0.0 + 73.125 2.25x + x2 = 0.0 + 73.125 Combine like terms: 0.0 + 73.125 = 73.125 2.25x + x2 = 73.125 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 73.125 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 73.125 + 1.265625 Combine like terms: 73.125 + 1.265625 = 74.390625 1.265625 + 2.25x + x2 = 74.390625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 74.390625 Calculate the square root of the right side: 8.625 Break this problem into two subproblems by setting (x + 1.125) equal to 8.625 and -8.625.Subproblem 1
x + 1.125 = 8.625 Simplifying x + 1.125 = 8.625 Reorder the terms: 1.125 + x = 8.625 Solving 1.125 + x = 8.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 8.625 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 8.625 + -1.125 x = 8.625 + -1.125 Combine like terms: 8.625 + -1.125 = 7.5 x = 7.5 Simplifying x = 7.5Subproblem 2
x + 1.125 = -8.625 Simplifying x + 1.125 = -8.625 Reorder the terms: 1.125 + x = -8.625 Solving 1.125 + x = -8.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -8.625 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -8.625 + -1.125 x = -8.625 + -1.125 Combine like terms: -8.625 + -1.125 = -9.75 x = -9.75 Simplifying x = -9.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.5, -9.75}
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