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Simplifying 8x2 + -14x + -100 = 0 Reorder the terms: -100 + -14x + 8x2 = 0 Solving -100 + -14x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + -7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + -7x + 4x2)' equal to zero and attempt to solve: Simplifying -50 + -7x + 4x2 = 0 Solving -50 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.5 + -1.75x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -1.75x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -1.75x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -1.75x + x2 = 0 + 12.5 -1.75x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -1.75x + x2 = 12.5 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 12.5 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 12.5 + 0.765625 Combine like terms: 12.5 + 0.765625 = 13.265625 0.765625 + -1.75x + x2 = 13.265625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 13.265625 Calculate the square root of the right side: 3.642200571 Break this problem into two subproblems by setting (x + -0.875) equal to 3.642200571 and -3.642200571.Subproblem 1
x + -0.875 = 3.642200571 Simplifying x + -0.875 = 3.642200571 Reorder the terms: -0.875 + x = 3.642200571 Solving -0.875 + x = 3.642200571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 3.642200571 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 3.642200571 + 0.875 x = 3.642200571 + 0.875 Combine like terms: 3.642200571 + 0.875 = 4.517200571 x = 4.517200571 Simplifying x = 4.517200571Subproblem 2
x + -0.875 = -3.642200571 Simplifying x + -0.875 = -3.642200571 Reorder the terms: -0.875 + x = -3.642200571 Solving -0.875 + x = -3.642200571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -3.642200571 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -3.642200571 + 0.875 x = -3.642200571 + 0.875 Combine like terms: -3.642200571 + 0.875 = -2.767200571 x = -2.767200571 Simplifying x = -2.767200571Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.517200571, -2.767200571}Solution
x = {4.517200571, -2.767200571}
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