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Simplifying x2 + -19x + 90.25 = 0 Reorder the terms: 90.25 + -19x + x2 = 0 Solving 90.25 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90.25' to each side of the equation. 90.25 + -19x + -90.25 + x2 = 0 + -90.25 Reorder the terms: 90.25 + -90.25 + -19x + x2 = 0 + -90.25 Combine like terms: 90.25 + -90.25 = 0.00 0.00 + -19x + x2 = 0 + -90.25 -19x + x2 = 0 + -90.25 Combine like terms: 0 + -90.25 = -90.25 -19x + x2 = -90.25 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 = -90.25 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -90.25 + 90.25 Combine like terms: -90.25 + 90.25 = 0.00 90.25 + -19x + x2 = 0.00 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -9.5) equal to 0.00 and 0.00.Subproblem 1
x + -9.5 = 0.00 Simplifying x + -9.5 = 0.00 Reorder the terms: -9.5 + x = 0.00 Solving -9.5 + x = 0.00 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 = 0.00 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 0.00 + 9.5 x = 0.00 + 9.5 Combine like terms: 0.00 + 9.5 = 9.5 x = 9.5 Simplifying x = 9.5Subproblem 2
x + -9.5 = 0.00 Simplifying x + -9.5 = 0.00 Reorder the terms: -9.5 + x = 0.00 Solving -9.5 + x = 0.00 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 = 0.00 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 0.00 + 9.5 x = 0.00 + 9.5 Combine like terms: 0.00 + 9.5 = 9.5 x = 9.5 Simplifying x = 9.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.5, 9.5}
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