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Simplifying 0.5x(x + 4) + 0.25 = 8 Reorder the terms: 0.5x(4 + x) + 0.25 = 8 (4 * 0.5x + x * 0.5x) + 0.25 = 8 (2x + 0.5x2) + 0.25 = 8 Reorder the terms: 0.25 + 2x + 0.5x2 = 8 Solving 0.25 + 2x + 0.5x2 = 8 Solving for variable 'x'. Reorder the terms: 0.25 + -8 + 2x + 0.5x2 = 8 + -8 Combine like terms: 0.25 + -8 = -7.75 -7.75 + 2x + 0.5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -7.75 + 2x + 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'. -15.5 + 4x + x2 = 0 Move the constant term to the right: Add '15.5' to each side of the equation. -15.5 + 4x + 15.5 + x2 = 0 + 15.5 Reorder the terms: -15.5 + 15.5 + 4x + x2 = 0 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + 4x + x2 = 0 + 15.5 4x + x2 = 0 + 15.5 Combine like terms: 0 + 15.5 = 15.5 4x + x2 = 15.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 15.5 + 4 Reorder the terms: 4 + 4x + x2 = 15.5 + 4 Combine like terms: 15.5 + 4 = 19.5 4 + 4x + x2 = 19.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (x + 2) equal to 4.415880433 and -4.415880433.Subproblem 1
x + 2 = 4.415880433 Simplifying x + 2 = 4.415880433 Reorder the terms: 2 + x = 4.415880433 Solving 2 + x = 4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.415880433 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.415880433 + -2 x = 4.415880433 + -2 Combine like terms: 4.415880433 + -2 = 2.415880433 x = 2.415880433 Simplifying x = 2.415880433Subproblem 2
x + 2 = -4.415880433 Simplifying x + 2 = -4.415880433 Reorder the terms: 2 + x = -4.415880433 Solving 2 + x = -4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.415880433 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.415880433 + -2 x = -4.415880433 + -2 Combine like terms: -4.415880433 + -2 = -6.415880433 x = -6.415880433 Simplifying x = -6.415880433Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.415880433, -6.415880433}
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