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Simplifying 4x2 + 525x + 625 = 0 Reorder the terms: 625 + 525x + 4x2 = 0 Solving 625 + 525x + 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'. 156.25 + 131.25x + x2 = 0 Move the constant term to the right: Add '-156.25' to each side of the equation. 156.25 + 131.25x + -156.25 + x2 = 0 + -156.25 Reorder the terms: 156.25 + -156.25 + 131.25x + x2 = 0 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 0.00 + 131.25x + x2 = 0 + -156.25 131.25x + x2 = 0 + -156.25 Combine like terms: 0 + -156.25 = -156.25 131.25x + x2 = -156.25 The x term is 131.25x. Take half its coefficient (65.625). Square it (4306.640625) and add it to both sides. Add '4306.640625' to each side of the equation. 131.25x + 4306.640625 + x2 = -156.25 + 4306.640625 Reorder the terms: 4306.640625 + 131.25x + x2 = -156.25 + 4306.640625 Combine like terms: -156.25 + 4306.640625 = 4150.390625 4306.640625 + 131.25x + x2 = 4150.390625 Factor a perfect square on the left side: (x + 65.625)(x + 65.625) = 4150.390625 Calculate the square root of the right side: 64.4235254 Break this problem into two subproblems by setting (x + 65.625) equal to 64.4235254 and -64.4235254.Subproblem 1
x + 65.625 = 64.4235254 Simplifying x + 65.625 = 64.4235254 Reorder the terms: 65.625 + x = 64.4235254 Solving 65.625 + x = 64.4235254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65.625' to each side of the equation. 65.625 + -65.625 + x = 64.4235254 + -65.625 Combine like terms: 65.625 + -65.625 = 0.000 0.000 + x = 64.4235254 + -65.625 x = 64.4235254 + -65.625 Combine like terms: 64.4235254 + -65.625 = -1.2014746 x = -1.2014746 Simplifying x = -1.2014746Subproblem 2
x + 65.625 = -64.4235254 Simplifying x + 65.625 = -64.4235254 Reorder the terms: 65.625 + x = -64.4235254 Solving 65.625 + x = -64.4235254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65.625' to each side of the equation. 65.625 + -65.625 + x = -64.4235254 + -65.625 Combine like terms: 65.625 + -65.625 = 0.000 0.000 + x = -64.4235254 + -65.625 x = -64.4235254 + -65.625 Combine like terms: -64.4235254 + -65.625 = -130.0485254 x = -130.0485254 Simplifying x = -130.0485254Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.2014746, -130.0485254}
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