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Simplifying x2 + 9.5x + -3 = 90 Reorder the terms: -3 + 9.5x + x2 = 90 Solving -3 + 9.5x + x2 = 90 Solving for variable 'x'. Reorder the terms: -3 + -90 + 9.5x + x2 = 90 + -90 Combine like terms: -3 + -90 = -93 -93 + 9.5x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -93 + 9.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '93' to each side of the equation. -93 + 9.5x + 93 + x2 = 0 + 93 Reorder the terms: -93 + 93 + 9.5x + x2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + 9.5x + x2 = 0 + 93 9.5x + x2 = 0 + 93 Combine like terms: 0 + 93 = 93 9.5x + x2 = 93 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 93 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 93 + 22.5625 Combine like terms: 93 + 22.5625 = 115.5625 22.5625 + 9.5x + x2 = 115.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 115.5625 Calculate the square root of the right side: 10.75 Break this problem into two subproblems by setting (x + 4.75) equal to 10.75 and -10.75.Subproblem 1
x + 4.75 = 10.75 Simplifying x + 4.75 = 10.75 Reorder the terms: 4.75 + x = 10.75 Solving 4.75 + x = 10.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 10.75 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 10.75 + -4.75 x = 10.75 + -4.75 Combine like terms: 10.75 + -4.75 = 6 x = 6 Simplifying x = 6Subproblem 2
x + 4.75 = -10.75 Simplifying x + 4.75 = -10.75 Reorder the terms: 4.75 + x = -10.75 Solving 4.75 + x = -10.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -10.75 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -10.75 + -4.75 x = -10.75 + -4.75 Combine like terms: -10.75 + -4.75 = -15.5 x = -15.5 Simplifying x = -15.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, -15.5}
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