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Simplifying 4x2 + 47x + -90 = 0 Reorder the terms: -90 + 47x + 4x2 = 0 Solving -90 + 47x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -22.5 + 11.75x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 11.75x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 11.75x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 11.75x + x2 = 0 + 22.5 11.75x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 11.75x + x2 = 22.5 The x term is 11.75x. Take half its coefficient (5.875). Square it (34.515625) and add it to both sides. Add '34.515625' to each side of the equation. 11.75x + 34.515625 + x2 = 22.5 + 34.515625 Reorder the terms: 34.515625 + 11.75x + x2 = 22.5 + 34.515625 Combine like terms: 22.5 + 34.515625 = 57.015625 34.515625 + 11.75x + x2 = 57.015625 Factor a perfect square on the left side: (x + 5.875)(x + 5.875) = 57.015625 Calculate the square root of the right side: 7.550869155 Break this problem into two subproblems by setting (x + 5.875) equal to 7.550869155 and -7.550869155.Subproblem 1
x + 5.875 = 7.550869155 Simplifying x + 5.875 = 7.550869155 Reorder the terms: 5.875 + x = 7.550869155 Solving 5.875 + x = 7.550869155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.875' to each side of the equation. 5.875 + -5.875 + x = 7.550869155 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + x = 7.550869155 + -5.875 x = 7.550869155 + -5.875 Combine like terms: 7.550869155 + -5.875 = 1.675869155 x = 1.675869155 Simplifying x = 1.675869155Subproblem 2
x + 5.875 = -7.550869155 Simplifying x + 5.875 = -7.550869155 Reorder the terms: 5.875 + x = -7.550869155 Solving 5.875 + x = -7.550869155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.875' to each side of the equation. 5.875 + -5.875 + x = -7.550869155 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + x = -7.550869155 + -5.875 x = -7.550869155 + -5.875 Combine like terms: -7.550869155 + -5.875 = -13.425869155 x = -13.425869155 Simplifying x = -13.425869155Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.675869155, -13.425869155}
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