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Simplifying 2x2 + 18 + x + -2x + 18 = 89 Reorder the terms: 18 + 18 + x + -2x + 2x2 = 89 Combine like terms: 18 + 18 = 36 36 + x + -2x + 2x2 = 89 Combine like terms: x + -2x = -1x 36 + -1x + 2x2 = 89 Solving 36 + -1x + 2x2 = 89 Solving for variable 'x'. Reorder the terms: 36 + -89 + -1x + 2x2 = 89 + -89 Combine like terms: 36 + -89 = -53 -53 + -1x + 2x2 = 89 + -89 Combine like terms: 89 + -89 = 0 -53 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -26.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '26.5' to each side of the equation. -26.5 + -0.5x + 26.5 + x2 = 0 + 26.5 Reorder the terms: -26.5 + 26.5 + -0.5x + x2 = 0 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + -0.5x + x2 = 0 + 26.5 -0.5x + x2 = 0 + 26.5 Combine like terms: 0 + 26.5 = 26.5 -0.5x + x2 = 26.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 26.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 26.5 + 0.0625 Combine like terms: 26.5 + 0.0625 = 26.5625 0.0625 + -0.5x + x2 = 26.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (x + -0.25) equal to 5.153882032 and -5.153882032.Subproblem 1
x + -0.25 = 5.153882032 Simplifying x + -0.25 = 5.153882032 Reorder the terms: -0.25 + x = 5.153882032 Solving -0.25 + x = 5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 5.153882032 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.153882032 + 0.25 x = 5.153882032 + 0.25 Combine like terms: 5.153882032 + 0.25 = 5.403882032 x = 5.403882032 Simplifying x = 5.403882032Subproblem 2
x + -0.25 = -5.153882032 Simplifying x + -0.25 = -5.153882032 Reorder the terms: -0.25 + x = -5.153882032 Solving -0.25 + x = -5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -5.153882032 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.153882032 + 0.25 x = -5.153882032 + 0.25 Combine like terms: -5.153882032 + 0.25 = -4.903882032 x = -4.903882032 Simplifying x = -4.903882032Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.403882032, -4.903882032}
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