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Simplifying 4x2 + 12.5x + 9 = 0 Reorder the terms: 9 + 12.5x + 4x2 = 0 Solving 9 + 12.5x + 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'. 2.25 + 3.125x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 3.125x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 3.125x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 3.125x + x2 = 0 + -2.25 3.125x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 3.125x + x2 = -2.25 The x term is 3.125x. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125x + 2.44140625 + x2 = -2.25 + 2.44140625 Reorder the terms: 2.44140625 + 3.125x + x2 = -2.25 + 2.44140625 Combine like terms: -2.25 + 2.44140625 = 0.19140625 2.44140625 + 3.125x + x2 = 0.19140625 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = 0.19140625 Calculate the square root of the right side: 0.4375 Break this problem into two subproblems by setting (x + 1.5625) equal to 0.4375 and -0.4375.Subproblem 1
x + 1.5625 = 0.4375 Simplifying x + 1.5625 = 0.4375 Reorder the terms: 1.5625 + x = 0.4375 Solving 1.5625 + x = 0.4375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = 0.4375 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 0.4375 + -1.5625 x = 0.4375 + -1.5625 Combine like terms: 0.4375 + -1.5625 = -1.125 x = -1.125 Simplifying x = -1.125Subproblem 2
x + 1.5625 = -0.4375 Simplifying x + 1.5625 = -0.4375 Reorder the terms: 1.5625 + x = -0.4375 Solving 1.5625 + x = -0.4375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = -0.4375 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -0.4375 + -1.5625 x = -0.4375 + -1.5625 Combine like terms: -0.4375 + -1.5625 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.125, -2}
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