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Simplifying 14x2 + 10x + -8 = 0 Reorder the terms: -8 + 10x + 14x2 = 0 Solving -8 + 10x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 5x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 5x + 7x2)' equal to zero and attempt to solve: Simplifying -4 + 5x + 7x2 = 0 Solving -4 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.7142857143x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.7142857143x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.7142857143x + x2 = 0 + 0.5714285714 0.7142857143x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.7142857143x + x2 = 0.5714285714 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 0.5714285714 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 0.5714285714 + 0.1275510204 Combine like terms: 0.5714285714 + 0.1275510204 = 0.6989795918 0.1275510204 + 0.7142857143x + x2 = 0.6989795918 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 0.6989795918 Calculate the square root of the right side: 0.836049994 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 0.836049994 and -0.836049994.Subproblem 1
x + 0.3571428572 = 0.836049994 Simplifying x + 0.3571428572 = 0.836049994 Reorder the terms: 0.3571428572 + x = 0.836049994 Solving 0.3571428572 + x = 0.836049994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 0.836049994 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 0.836049994 + -0.3571428572 x = 0.836049994 + -0.3571428572 Combine like terms: 0.836049994 + -0.3571428572 = 0.4789071368 x = 0.4789071368 Simplifying x = 0.4789071368Subproblem 2
x + 0.3571428572 = -0.836049994 Simplifying x + 0.3571428572 = -0.836049994 Reorder the terms: 0.3571428572 + x = -0.836049994 Solving 0.3571428572 + x = -0.836049994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -0.836049994 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -0.836049994 + -0.3571428572 x = -0.836049994 + -0.3571428572 Combine like terms: -0.836049994 + -0.3571428572 = -1.1931928512 x = -1.1931928512 Simplifying x = -1.1931928512Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4789071368, -1.1931928512}Solution
x = {0.4789071368, -1.1931928512}
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