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Simplifying 4(x2 + -25x + -425) = 0 Reorder the terms: 4(-425 + -25x + x2) = 0 (-425 * 4 + -25x * 4 + x2 * 4) = 0 (-1700 + -100x + 4x2) = 0 Solving -1700 + -100x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-425 + -25x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-425 + -25x + x2)' equal to zero and attempt to solve: Simplifying -425 + -25x + x2 = 0 Solving -425 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '425' to each side of the equation. -425 + -25x + 425 + x2 = 0 + 425 Reorder the terms: -425 + 425 + -25x + x2 = 0 + 425 Combine like terms: -425 + 425 = 0 0 + -25x + x2 = 0 + 425 -25x + x2 = 0 + 425 Combine like terms: 0 + 425 = 425 -25x + x2 = 425 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 425 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 425 + 156.25 Combine like terms: 425 + 156.25 = 581.25 156.25 + -25x + x2 = 581.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 581.25 Calculate the square root of the right side: 24.109126902 Break this problem into two subproblems by setting (x + -12.5) equal to 24.109126902 and -24.109126902.Subproblem 1
x + -12.5 = 24.109126902 Simplifying x + -12.5 = 24.109126902 Reorder the terms: -12.5 + x = 24.109126902 Solving -12.5 + x = 24.109126902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 24.109126902 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 24.109126902 + 12.5 x = 24.109126902 + 12.5 Combine like terms: 24.109126902 + 12.5 = 36.609126902 x = 36.609126902 Simplifying x = 36.609126902Subproblem 2
x + -12.5 = -24.109126902 Simplifying x + -12.5 = -24.109126902 Reorder the terms: -12.5 + x = -24.109126902 Solving -12.5 + x = -24.109126902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -24.109126902 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -24.109126902 + 12.5 x = -24.109126902 + 12.5 Combine like terms: -24.109126902 + 12.5 = -11.609126902 x = -11.609126902 Simplifying x = -11.609126902Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.609126902, -11.609126902}Solution
x = {36.609126902, -11.609126902}
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