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Simplifying 8x2 + 14x = 50 Reorder the terms: 14x + 8x2 = 50 Solving 14x + 8x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 14x + 8x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 14x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying -25 + 7x + 4x2 = 0 Solving -25 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 1.75x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 1.75x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 1.75x + x2 = 0 + 6.25 1.75x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 1.75x + x2 = 6.25 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 = 6.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 6.25 + 0.765625 Combine like terms: 6.25 + 0.765625 = 7.015625 0.765625 + 1.75x + x2 = 7.015625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 7.015625 Calculate the square root of the right side: 2.648702513 Break this problem into two subproblems by setting (x + 0.875) equal to 2.648702513 and -2.648702513.Subproblem 1
x + 0.875 = 2.648702513 Simplifying x + 0.875 = 2.648702513 Reorder the terms: 0.875 + x = 2.648702513 Solving 0.875 + x = 2.648702513 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 = 2.648702513 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.648702513 + -0.875 x = 2.648702513 + -0.875 Combine like terms: 2.648702513 + -0.875 = 1.773702513 x = 1.773702513 Simplifying x = 1.773702513Subproblem 2
x + 0.875 = -2.648702513 Simplifying x + 0.875 = -2.648702513 Reorder the terms: 0.875 + x = -2.648702513 Solving 0.875 + x = -2.648702513 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 = -2.648702513 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.648702513 + -0.875 x = -2.648702513 + -0.875 Combine like terms: -2.648702513 + -0.875 = -3.523702513 x = -3.523702513 Simplifying x = -3.523702513Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.773702513, -3.523702513}Solution
x = {1.773702513, -3.523702513}
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