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Simplifying 25x2 + 140x + 125 = 360 Reorder the terms: 125 + 140x + 25x2 = 360 Solving 125 + 140x + 25x2 = 360 Solving for variable 'x'. Reorder the terms: 125 + -360 + 140x + 25x2 = 360 + -360 Combine like terms: 125 + -360 = -235 -235 + 140x + 25x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -235 + 140x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-47 + 28x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-47 + 28x + 5x2)' equal to zero and attempt to solve: Simplifying -47 + 28x + 5x2 = 0 Solving -47 + 28x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.4 + 5.6x + x2 = 0 Move the constant term to the right: Add '9.4' to each side of the equation. -9.4 + 5.6x + 9.4 + x2 = 0 + 9.4 Reorder the terms: -9.4 + 9.4 + 5.6x + x2 = 0 + 9.4 Combine like terms: -9.4 + 9.4 = 0.0 0.0 + 5.6x + x2 = 0 + 9.4 5.6x + x2 = 0 + 9.4 Combine like terms: 0 + 9.4 = 9.4 5.6x + x2 = 9.4 The x term is 5.6x. Take half its coefficient (2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. 5.6x + 7.84 + x2 = 9.4 + 7.84 Reorder the terms: 7.84 + 5.6x + x2 = 9.4 + 7.84 Combine like terms: 9.4 + 7.84 = 17.24 7.84 + 5.6x + x2 = 17.24 Factor a perfect square on the left side: (x + 2.8)(x + 2.8) = 17.24 Calculate the square root of the right side: 4.152107898 Break this problem into two subproblems by setting (x + 2.8) equal to 4.152107898 and -4.152107898.Subproblem 1
x + 2.8 = 4.152107898 Simplifying x + 2.8 = 4.152107898 Reorder the terms: 2.8 + x = 4.152107898 Solving 2.8 + x = 4.152107898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = 4.152107898 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 4.152107898 + -2.8 x = 4.152107898 + -2.8 Combine like terms: 4.152107898 + -2.8 = 1.352107898 x = 1.352107898 Simplifying x = 1.352107898Subproblem 2
x + 2.8 = -4.152107898 Simplifying x + 2.8 = -4.152107898 Reorder the terms: 2.8 + x = -4.152107898 Solving 2.8 + x = -4.152107898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = -4.152107898 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -4.152107898 + -2.8 x = -4.152107898 + -2.8 Combine like terms: -4.152107898 + -2.8 = -6.952107898 x = -6.952107898 Simplifying x = -6.952107898Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.352107898, -6.952107898}Solution
x = {1.352107898, -6.952107898}
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