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Simplifying 0 = 14x2 + 56x + -200 Reorder the terms: 0 = -200 + 56x + 14x2 Solving 0 = -200 + 56x + 14x2 Solving for variable 'x'. Combine like terms: 0 + 200 = 200 200 + -56x + -14x2 = -200 + 56x + 14x2 + 200 + -56x + -14x2 Reorder the terms: 200 + -56x + -14x2 = -200 + 200 + 56x + -56x + 14x2 + -14x2 Combine like terms: -200 + 200 = 0 200 + -56x + -14x2 = 0 + 56x + -56x + 14x2 + -14x2 200 + -56x + -14x2 = 56x + -56x + 14x2 + -14x2 Combine like terms: 56x + -56x = 0 200 + -56x + -14x2 = 0 + 14x2 + -14x2 200 + -56x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 200 + -56x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(100 + -28x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(100 + -28x + -7x2)' equal to zero and attempt to solve: Simplifying 100 + -28x + -7x2 = 0 Solving 100 + -28x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -14.28571429 + 4x + x2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + 4x + 14.28571429 + x2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + 4x + x2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + 4x + x2 = 0 + 14.28571429 4x + x2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 4x + x2 = 14.28571429 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 14.28571429 + 4 Reorder the terms: 4 + 4x + x2 = 14.28571429 + 4 Combine like terms: 14.28571429 + 4 = 18.28571429 4 + 4x + x2 = 18.28571429 Factor a perfect square on the left side: (x + 2)(x + 2) = 18.28571429 Calculate the square root of the right side: 4.276179871 Break this problem into two subproblems by setting (x + 2) equal to 4.276179871 and -4.276179871.Subproblem 1
x + 2 = 4.276179871 Simplifying x + 2 = 4.276179871 Reorder the terms: 2 + x = 4.276179871 Solving 2 + x = 4.276179871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.276179871 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.276179871 + -2 x = 4.276179871 + -2 Combine like terms: 4.276179871 + -2 = 2.276179871 x = 2.276179871 Simplifying x = 2.276179871Subproblem 2
x + 2 = -4.276179871 Simplifying x + 2 = -4.276179871 Reorder the terms: 2 + x = -4.276179871 Solving 2 + x = -4.276179871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.276179871 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.276179871 + -2 x = -4.276179871 + -2 Combine like terms: -4.276179871 + -2 = -6.276179871 x = -6.276179871 Simplifying x = -6.276179871Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.276179871, -6.276179871}Solution
x = {2.276179871, -6.276179871}
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