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Simplifying x2 + -19x + -7 = 0 Reorder the terms: -7 + -19x + x2 = 0 Solving -7 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -19x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -19x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -19x + x2 = 0 + 7 -19x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -19x + x2 = 7 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 7 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 7 + 90.25 Combine like terms: 7 + 90.25 = 97.25 90.25 + -19x + x2 = 97.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 97.25 Calculate the square root of the right side: 9.861541462 Break this problem into two subproblems by setting (x + -9.5) equal to 9.861541462 and -9.861541462.Subproblem 1
x + -9.5 = 9.861541462 Simplifying x + -9.5 = 9.861541462 Reorder the terms: -9.5 + x = 9.861541462 Solving -9.5 + x = 9.861541462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 9.861541462 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.861541462 + 9.5 x = 9.861541462 + 9.5 Combine like terms: 9.861541462 + 9.5 = 19.361541462 x = 19.361541462 Simplifying x = 19.361541462Subproblem 2
x + -9.5 = -9.861541462 Simplifying x + -9.5 = -9.861541462 Reorder the terms: -9.5 + x = -9.861541462 Solving -9.5 + x = -9.861541462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -9.861541462 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.861541462 + 9.5 x = -9.861541462 + 9.5 Combine like terms: -9.861541462 + 9.5 = -0.361541462 x = -0.361541462 Simplifying x = -0.361541462Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.361541462, -0.361541462}
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