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Simplifying 4(7x2 + 4x + -6) = 0 Reorder the terms: 4(-6 + 4x + 7x2) = 0 (-6 * 4 + 4x * 4 + 7x2 * 4) = 0 (-24 + 16x + 28x2) = 0 Solving -24 + 16x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 4x + 7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + 4x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + 4x + 7x2 = 0 Solving -6 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 0.5714285714x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 0.5714285714x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + 0.8571428571 0.5714285714x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 0.5714285714x + x2 = 0.8571428571 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 0.8571428571 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.8571428571 + 0.08163265305 Combine like terms: 0.8571428571 + 0.08163265305 = 0.93877551015 0.08163265305 + 0.5714285714x + x2 = 0.93877551015 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.93877551015 Calculate the square root of the right side: 0.968904283 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.968904283 and -0.968904283.Subproblem 1
x + 0.2857142857 = 0.968904283 Simplifying x + 0.2857142857 = 0.968904283 Reorder the terms: 0.2857142857 + x = 0.968904283 Solving 0.2857142857 + x = 0.968904283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 0.968904283 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.968904283 + -0.2857142857 x = 0.968904283 + -0.2857142857 Combine like terms: 0.968904283 + -0.2857142857 = 0.6831899973 x = 0.6831899973 Simplifying x = 0.6831899973Subproblem 2
x + 0.2857142857 = -0.968904283 Simplifying x + 0.2857142857 = -0.968904283 Reorder the terms: 0.2857142857 + x = -0.968904283 Solving 0.2857142857 + x = -0.968904283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -0.968904283 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.968904283 + -0.2857142857 x = -0.968904283 + -0.2857142857 Combine like terms: -0.968904283 + -0.2857142857 = -1.2546185687 x = -1.2546185687 Simplifying x = -1.2546185687Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6831899973, -1.2546185687}Solution
x = {0.6831899973, -1.2546185687}
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