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Simplifying 0.5x2 + x + -2.5 = 15 Reorder the terms: -2.5 + x + 0.5x2 = 15 Solving -2.5 + x + 0.5x2 = 15 Solving for variable 'x'. Reorder the terms: -2.5 + -15 + x + 0.5x2 = 15 + -15 Combine like terms: -2.5 + -15 = -17.5 -17.5 + x + 0.5x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -17.5 + x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -35 + 2x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 2x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 2x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 2x + x2 = 0 + 35 2x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 2x + x2 = 35 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. 2x + 0.25 + x2 = 35 + 0.25 Reorder the terms: 0.25 + 2x + x2 = 35 + 0.25 Combine like terms: 35 + 0.25 = 35.25 0.25 + 2x + x2 = 35.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + 0.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + 0.5 = 5.937171044 Simplifying x + 0.5 = 5.937171044 Reorder the terms: 0.5 + x = 5.937171044 Solving 0.5 + x = 5.937171044 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 = 5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.937171044 + -0.5 x = 5.937171044 + -0.5 Combine like terms: 5.937171044 + -0.5 = 5.437171044 x = 5.437171044 Simplifying x = 5.437171044Subproblem 2
x + 0.5 = -5.937171044 Simplifying x + 0.5 = -5.937171044 Reorder the terms: 0.5 + x = -5.937171044 Solving 0.5 + x = -5.937171044 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 = -5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.937171044 + -0.5 x = -5.937171044 + -0.5 Combine like terms: -5.937171044 + -0.5 = -6.437171044 x = -6.437171044 Simplifying x = -6.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.437171044, -6.437171044}
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