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Simplifying 2.5x2 + x = 84 Reorder the terms: x + 2.5x2 = 84 Solving x + 2.5x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + x + 2.5x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + x + 2.5x2 = 0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -33.6 + 0.4x + x2 = 0 Move the constant term to the right: Add '33.6' to each side of the equation. -33.6 + 0.4x + 33.6 + x2 = 0 + 33.6 Reorder the terms: -33.6 + 33.6 + 0.4x + x2 = 0 + 33.6 Combine like terms: -33.6 + 33.6 = 0.0 0.0 + 0.4x + x2 = 0 + 33.6 0.4x + x2 = 0 + 33.6 Combine like terms: 0 + 33.6 = 33.6 0.4x + x2 = 33.6 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. 0.4x + 0.25 + x2 = 33.6 + 0.25 Reorder the terms: 0.25 + 0.4x + x2 = 33.6 + 0.25 Combine like terms: 33.6 + 0.25 = 33.85 0.25 + 0.4x + x2 = 33.85 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 33.85 Calculate the square root of the right side: 5.818075283 Break this problem into two subproblems by setting (x + 0.5) equal to 5.818075283 and -5.818075283.Subproblem 1
x + 0.5 = 5.818075283 Simplifying x + 0.5 = 5.818075283 Reorder the terms: 0.5 + x = 5.818075283 Solving 0.5 + x = 5.818075283 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 = 5.818075283 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.818075283 + -0.5 x = 5.818075283 + -0.5 Combine like terms: 5.818075283 + -0.5 = 5.318075283 x = 5.318075283 Simplifying x = 5.318075283Subproblem 2
x + 0.5 = -5.818075283 Simplifying x + 0.5 = -5.818075283 Reorder the terms: 0.5 + x = -5.818075283 Solving 0.5 + x = -5.818075283 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 = -5.818075283 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.818075283 + -0.5 x = -5.818075283 + -0.5 Combine like terms: -5.818075283 + -0.5 = -6.318075283 x = -6.318075283 Simplifying x = -6.318075283Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.318075283, -6.318075283}
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