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Simplifying x2 + -63x + 90 = 0 Reorder the terms: 90 + -63x + x2 = 0 Solving 90 + -63x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + -63x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -63x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -63x + x2 = 0 + -90 -63x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -63x + x2 = -90 The x term is -63x. Take half its coefficient (-31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. -63x + 992.25 + x2 = -90 + 992.25 Reorder the terms: 992.25 + -63x + x2 = -90 + 992.25 Combine like terms: -90 + 992.25 = 902.25 992.25 + -63x + x2 = 902.25 Factor a perfect square on the left side: (x + -31.5)(x + -31.5) = 902.25 Calculate the square root of the right side: 30.037476592 Break this problem into two subproblems by setting (x + -31.5) equal to 30.037476592 and -30.037476592.Subproblem 1
x + -31.5 = 30.037476592 Simplifying x + -31.5 = 30.037476592 Reorder the terms: -31.5 + x = 30.037476592 Solving -31.5 + x = 30.037476592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + x = 30.037476592 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = 30.037476592 + 31.5 x = 30.037476592 + 31.5 Combine like terms: 30.037476592 + 31.5 = 61.537476592 x = 61.537476592 Simplifying x = 61.537476592Subproblem 2
x + -31.5 = -30.037476592 Simplifying x + -31.5 = -30.037476592 Reorder the terms: -31.5 + x = -30.037476592 Solving -31.5 + x = -30.037476592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + x = -30.037476592 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = -30.037476592 + 31.5 x = -30.037476592 + 31.5 Combine like terms: -30.037476592 + 31.5 = 1.462523408 x = 1.462523408 Simplifying x = 1.462523408Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.537476592, 1.462523408}
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