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Simplifying 90 + -1x2 + -19x + 90 = 100 Reorder the terms: 90 + 90 + -19x + -1x2 = 100 Combine like terms: 90 + 90 = 180 180 + -19x + -1x2 = 100 Solving 180 + -19x + -1x2 = 100 Solving for variable 'x'. Reorder the terms: 180 + -100 + -19x + -1x2 = 100 + -100 Combine like terms: 180 + -100 = 80 80 + -19x + -1x2 = 100 + -100 Combine like terms: 100 + -100 = 0 80 + -19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + 19x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 19x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 19x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 19x + x2 = 0 + 80 19x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 19x + x2 = 80 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 = 80 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 80 + 90.25 Combine like terms: 80 + 90.25 = 170.25 90.25 + 19x + x2 = 170.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (x + 9.5) equal to 13.047988351 and -13.047988351.Subproblem 1
x + 9.5 = 13.047988351 Simplifying x + 9.5 = 13.047988351 Reorder the terms: 9.5 + x = 13.047988351 Solving 9.5 + x = 13.047988351 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 = 13.047988351 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 13.047988351 + -9.5 x = 13.047988351 + -9.5 Combine like terms: 13.047988351 + -9.5 = 3.547988351 x = 3.547988351 Simplifying x = 3.547988351Subproblem 2
x + 9.5 = -13.047988351 Simplifying x + 9.5 = -13.047988351 Reorder the terms: 9.5 + x = -13.047988351 Solving 9.5 + x = -13.047988351 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 = -13.047988351 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -13.047988351 + -9.5 x = -13.047988351 + -9.5 Combine like terms: -13.047988351 + -9.5 = -22.547988351 x = -22.547988351 Simplifying x = -22.547988351Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.547988351, -22.547988351}
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