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Simplifying 0 = 7x2 + -54x + -52 Reorder the terms: 0 = -52 + -54x + 7x2 Solving 0 = -52 + -54x + 7x2 Solving for variable 'x'. Combine like terms: 0 + 52 = 52 52 + 54x + -7x2 = -52 + -54x + 7x2 + 52 + 54x + -7x2 Reorder the terms: 52 + 54x + -7x2 = -52 + 52 + -54x + 54x + 7x2 + -7x2 Combine like terms: -52 + 52 = 0 52 + 54x + -7x2 = 0 + -54x + 54x + 7x2 + -7x2 52 + 54x + -7x2 = -54x + 54x + 7x2 + -7x2 Combine like terms: -54x + 54x = 0 52 + 54x + -7x2 = 0 + 7x2 + -7x2 52 + 54x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 52 + 54x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -7.428571429 + -7.714285714x + x2 = 0 Move the constant term to the right: Add '7.428571429' to each side of the equation. -7.428571429 + -7.714285714x + 7.428571429 + x2 = 0 + 7.428571429 Reorder the terms: -7.428571429 + 7.428571429 + -7.714285714x + x2 = 0 + 7.428571429 Combine like terms: -7.428571429 + 7.428571429 = 0.000000000 0.000000000 + -7.714285714x + x2 = 0 + 7.428571429 -7.714285714x + x2 = 0 + 7.428571429 Combine like terms: 0 + 7.428571429 = 7.428571429 -7.714285714x + x2 = 7.428571429 The x term is -7.714285714x. Take half its coefficient (-3.857142857). Square it (14.87755102) and add it to both sides. Add '14.87755102' to each side of the equation. -7.714285714x + 14.87755102 + x2 = 7.428571429 + 14.87755102 Reorder the terms: 14.87755102 + -7.714285714x + x2 = 7.428571429 + 14.87755102 Combine like terms: 7.428571429 + 14.87755102 = 22.306122449 14.87755102 + -7.714285714x + x2 = 22.306122449 Factor a perfect square on the left side: (x + -3.857142857)(x + -3.857142857) = 22.306122449 Calculate the square root of the right side: 4.722935787 Break this problem into two subproblems by setting (x + -3.857142857) equal to 4.722935787 and -4.722935787.Subproblem 1
x + -3.857142857 = 4.722935787 Simplifying x + -3.857142857 = 4.722935787 Reorder the terms: -3.857142857 + x = 4.722935787 Solving -3.857142857 + x = 4.722935787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.857142857' to each side of the equation. -3.857142857 + 3.857142857 + x = 4.722935787 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + x = 4.722935787 + 3.857142857 x = 4.722935787 + 3.857142857 Combine like terms: 4.722935787 + 3.857142857 = 8.580078644 x = 8.580078644 Simplifying x = 8.580078644Subproblem 2
x + -3.857142857 = -4.722935787 Simplifying x + -3.857142857 = -4.722935787 Reorder the terms: -3.857142857 + x = -4.722935787 Solving -3.857142857 + x = -4.722935787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.857142857' to each side of the equation. -3.857142857 + 3.857142857 + x = -4.722935787 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + x = -4.722935787 + 3.857142857 x = -4.722935787 + 3.857142857 Combine like terms: -4.722935787 + 3.857142857 = -0.86579293 x = -0.86579293 Simplifying x = -0.86579293Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.580078644, -0.86579293}
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