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Simplifying 7x2 + -4x + -52 = 0 Reorder the terms: -52 + -4x + 7x2 = 0 Solving -52 + -4x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -7.428571429 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '7.428571429' to each side of the equation. -7.428571429 + -0.5714285714x + 7.428571429 + x2 = 0 + 7.428571429 Reorder the terms: -7.428571429 + 7.428571429 + -0.5714285714x + x2 = 0 + 7.428571429 Combine like terms: -7.428571429 + 7.428571429 = 0.000000000 0.000000000 + -0.5714285714x + x2 = 0 + 7.428571429 -0.5714285714x + x2 = 0 + 7.428571429 Combine like terms: 0 + 7.428571429 = 7.428571429 -0.5714285714x + x2 = 7.428571429 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 = 7.428571429 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 7.428571429 + 0.08163265305 Combine like terms: 7.428571429 + 0.08163265305 = 7.51020408205 0.08163265305 + -0.5714285714x + x2 = 7.51020408205 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 7.51020408205 Calculate the square root of the right side: 2.740475156 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 2.740475156 and -2.740475156.Subproblem 1
x + -0.2857142857 = 2.740475156 Simplifying x + -0.2857142857 = 2.740475156 Reorder the terms: -0.2857142857 + x = 2.740475156 Solving -0.2857142857 + x = 2.740475156 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 = 2.740475156 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 2.740475156 + 0.2857142857 x = 2.740475156 + 0.2857142857 Combine like terms: 2.740475156 + 0.2857142857 = 3.0261894417 x = 3.0261894417 Simplifying x = 3.0261894417Subproblem 2
x + -0.2857142857 = -2.740475156 Simplifying x + -0.2857142857 = -2.740475156 Reorder the terms: -0.2857142857 + x = -2.740475156 Solving -0.2857142857 + x = -2.740475156 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 = -2.740475156 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -2.740475156 + 0.2857142857 x = -2.740475156 + 0.2857142857 Combine like terms: -2.740475156 + 0.2857142857 = -2.4547608703 x = -2.4547608703 Simplifying x = -2.4547608703Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0261894417, -2.4547608703}
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