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Simplifying 10x2 + 14x + -6 = 0 Reorder the terms: -6 + 14x + 10x2 = 0 Solving -6 + 14x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 7x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying -3 + 7x + 5x2 = 0 Solving -3 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 1.4x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 1.4x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 1.4x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 1.4x + x2 = 0 + 0.6 1.4x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 1.4x + x2 = 0.6 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 0.6 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 0.6 + 0.49 Combine like terms: 0.6 + 0.49 = 1.09 0.49 + 1.4x + x2 = 1.09 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 1.09 Calculate the square root of the right side: 1.044030651 Break this problem into two subproblems by setting (x + 0.7) equal to 1.044030651 and -1.044030651.Subproblem 1
x + 0.7 = 1.044030651 Simplifying x + 0.7 = 1.044030651 Reorder the terms: 0.7 + x = 1.044030651 Solving 0.7 + x = 1.044030651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 1.044030651 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 1.044030651 + -0.7 x = 1.044030651 + -0.7 Combine like terms: 1.044030651 + -0.7 = 0.344030651 x = 0.344030651 Simplifying x = 0.344030651Subproblem 2
x + 0.7 = -1.044030651 Simplifying x + 0.7 = -1.044030651 Reorder the terms: 0.7 + x = -1.044030651 Solving 0.7 + x = -1.044030651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -1.044030651 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -1.044030651 + -0.7 x = -1.044030651 + -0.7 Combine like terms: -1.044030651 + -0.7 = -1.744030651 x = -1.744030651 Simplifying x = -1.744030651Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.344030651, -1.744030651}Solution
x = {0.344030651, -1.744030651}
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