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Simplifying 25x2 + -15 + x = 9375x Reorder the terms: -15 + x + 25x2 = 9375x Solving -15 + x + 25x2 = 9375x Solving for variable 'x'. Reorder the terms: -15 + x + -9375x + 25x2 = 9375x + -9375x Combine like terms: x + -9375x = -9374x -15 + -9374x + 25x2 = 9375x + -9375x Combine like terms: 9375x + -9375x = 0 -15 + -9374x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.6 + -374.96x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -374.96x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -374.96x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -374.96x + x2 = 0 + 0.6 -374.96x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -374.96x + x2 = 0.6 The x term is -374.96x. Take half its coefficient (-187.48). Square it (35148.7504) and add it to both sides. Add '35148.7504' to each side of the equation. -374.96x + 35148.7504 + x2 = 0.6 + 35148.7504 Reorder the terms: 35148.7504 + -374.96x + x2 = 0.6 + 35148.7504 Combine like terms: 0.6 + 35148.7504 = 35149.3504 35148.7504 + -374.96x + x2 = 35149.3504 Factor a perfect square on the left side: (x + -187.48)(x + -187.48) = 35149.3504 Calculate the square root of the right side: 187.481600164 Break this problem into two subproblems by setting (x + -187.48) equal to 187.481600164 and -187.481600164.Subproblem 1
x + -187.48 = 187.481600164 Simplifying x + -187.48 = 187.481600164 Reorder the terms: -187.48 + x = 187.481600164 Solving -187.48 + x = 187.481600164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '187.48' to each side of the equation. -187.48 + 187.48 + x = 187.481600164 + 187.48 Combine like terms: -187.48 + 187.48 = 0.00 0.00 + x = 187.481600164 + 187.48 x = 187.481600164 + 187.48 Combine like terms: 187.481600164 + 187.48 = 374.961600164 x = 374.961600164 Simplifying x = 374.961600164Subproblem 2
x + -187.48 = -187.481600164 Simplifying x + -187.48 = -187.481600164 Reorder the terms: -187.48 + x = -187.481600164 Solving -187.48 + x = -187.481600164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '187.48' to each side of the equation. -187.48 + 187.48 + x = -187.481600164 + 187.48 Combine like terms: -187.48 + 187.48 = 0.00 0.00 + x = -187.481600164 + 187.48 x = -187.481600164 + 187.48 Combine like terms: -187.481600164 + 187.48 = -0.001600164 x = -0.001600164 Simplifying x = -0.001600164Solution
The solution to the problem is based on the solutions from the subproblems. x = {374.961600164, -0.001600164}
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