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Simplifying (2x2) + -7x + -76 = 0 Reorder the terms: -76 + -7x + (2x2) = 0 Solving -76 + -7x + (2x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -38 + -3.5x + x2 = 0 Move the constant term to the right: Add '38' to each side of the equation. -38 + -3.5x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -3.5x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -3.5x + x2 = 0 + 38 -3.5x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -3.5x + x2 = 38 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 38 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 38 + 3.0625 Combine like terms: 38 + 3.0625 = 41.0625 3.0625 + -3.5x + x2 = 41.0625 Factor a perfect square on the left side: ((x) + -1.75)((x) + -1.75) = 41.0625 Calculate the square root of the right side: 6.408002809 Break this problem into two subproblems by setting ((x) + -1.75) equal to 6.408002809 and -6.408002809.Subproblem 1
(x) + -1.75 = 6.408002809 Simplifying (x) + -1.75 = 6.408002809 x + -1.75 = 6.408002809 Reorder the terms: -1.75 + x = 6.408002809 Solving -1.75 + x = 6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 6.408002809 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 6.408002809 + 1.75 x = 6.408002809 + 1.75 Combine like terms: 6.408002809 + 1.75 = 8.158002809 x = 8.158002809 Simplifying x = 8.158002809Subproblem 2
(x) + -1.75 = -6.408002809 Simplifying (x) + -1.75 = -6.408002809 x + -1.75 = -6.408002809 Reorder the terms: -1.75 + x = -6.408002809 Solving -1.75 + x = -6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -6.408002809 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -6.408002809 + 1.75 x = -6.408002809 + 1.75 Combine like terms: -6.408002809 + 1.75 = -4.658002809 x = -4.658002809 Simplifying x = -4.658002809Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.158002809, -4.658002809}
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