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Simplifying -90 + 5x2 + -4 = 2x2 + -1x + -30 Reorder the terms: -90 + -4 + 5x2 = 2x2 + -1x + -30 Combine like terms: -90 + -4 = -94 -94 + 5x2 = 2x2 + -1x + -30 Reorder the terms: -94 + 5x2 = -30 + -1x + 2x2 Solving -94 + 5x2 = -30 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: -94 + 30 + x + 5x2 + -2x2 = -30 + -1x + 2x2 + 30 + x + -2x2 Combine like terms: -94 + 30 = -64 -64 + x + 5x2 + -2x2 = -30 + -1x + 2x2 + 30 + x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -64 + x + 3x2 = -30 + -1x + 2x2 + 30 + x + -2x2 Reorder the terms: -64 + x + 3x2 = -30 + 30 + -1x + x + 2x2 + -2x2 Combine like terms: -30 + 30 = 0 -64 + x + 3x2 = 0 + -1x + x + 2x2 + -2x2 -64 + x + 3x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 -64 + x + 3x2 = 0 + 2x2 + -2x2 -64 + x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -64 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21.33333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + 0.3333333333x + 21.33333333 + x2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + 0.3333333333x + x2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 21.33333333 0.3333333333x + x2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 0.3333333333x + x2 = 21.33333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 21.33333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 21.33333333 + 0.25 Combine like terms: 21.33333333 + 0.25 = 21.58333333 0.25 + 0.3333333333x + x2 = 21.58333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 21.58333333 Calculate the square root of the right side: 4.645786621 Break this problem into two subproblems by setting (x + 0.5) equal to 4.645786621 and -4.645786621.Subproblem 1
x + 0.5 = 4.645786621 Simplifying x + 0.5 = 4.645786621 Reorder the terms: 0.5 + x = 4.645786621 Solving 0.5 + x = 4.645786621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.645786621 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.645786621 + -0.5 x = 4.645786621 + -0.5 Combine like terms: 4.645786621 + -0.5 = 4.145786621 x = 4.145786621 Simplifying x = 4.145786621Subproblem 2
x + 0.5 = -4.645786621 Simplifying x + 0.5 = -4.645786621 Reorder the terms: 0.5 + x = -4.645786621 Solving 0.5 + x = -4.645786621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.645786621 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.645786621 + -0.5 x = -4.645786621 + -0.5 Combine like terms: -4.645786621 + -0.5 = -5.145786621 x = -5.145786621 Simplifying x = -5.145786621Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.145786621, -5.145786621}
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