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Simplifying x2 + -24x + 84 = 0 Reorder the terms: 84 + -24x + x2 = 0 Solving 84 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + -24x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + -24x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -24x + x2 = 0 + -84 -24x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 -24x + x2 = -84 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -84 + 144 Reorder the terms: 144 + -24x + x2 = -84 + 144 Combine like terms: -84 + 144 = 60 144 + -24x + x2 = 60 Factor a perfect square on the left side: (x + -12)(x + -12) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -12) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -12 = 7.745966692 Simplifying x + -12 = 7.745966692 Reorder the terms: -12 + x = 7.745966692 Solving -12 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 7.745966692 + 12 Combine like terms: -12 + 12 = 0 0 + x = 7.745966692 + 12 x = 7.745966692 + 12 Combine like terms: 7.745966692 + 12 = 19.745966692 x = 19.745966692 Simplifying x = 19.745966692Subproblem 2
x + -12 = -7.745966692 Simplifying x + -12 = -7.745966692 Reorder the terms: -12 + x = -7.745966692 Solving -12 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -7.745966692 + 12 Combine like terms: -12 + 12 = 0 0 + x = -7.745966692 + 12 x = -7.745966692 + 12 Combine like terms: -7.745966692 + 12 = 4.254033308 x = 4.254033308 Simplifying x = 4.254033308Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.745966692, 4.254033308}
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