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Simplifying 4x2 = 30 + x Solving 4x2 = 30 + x Solving for variable 'x'. Reorder the terms: -30 + -1x + 4x2 = 30 + x + -30 + -1x Reorder the terms: -30 + -1x + 4x2 = 30 + -30 + x + -1x Combine like terms: 30 + -30 = 0 -30 + -1x + 4x2 = 0 + x + -1x -30 + -1x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -30 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.5 + -0.25x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -0.25x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -0.25x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -0.25x + x2 = 0 + 7.5 -0.25x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -0.25x + x2 = 7.5 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 7.5 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 7.5 + 0.015625 Combine like terms: 7.5 + 0.015625 = 7.515625 0.015625 + -0.25x + x2 = 7.515625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 7.515625 Calculate the square root of the right side: 2.741464025 Break this problem into two subproblems by setting (x + -0.125) equal to 2.741464025 and -2.741464025.Subproblem 1
x + -0.125 = 2.741464025 Simplifying x + -0.125 = 2.741464025 Reorder the terms: -0.125 + x = 2.741464025 Solving -0.125 + x = 2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 2.741464025 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 2.741464025 + 0.125 x = 2.741464025 + 0.125 Combine like terms: 2.741464025 + 0.125 = 2.866464025 x = 2.866464025 Simplifying x = 2.866464025Subproblem 2
x + -0.125 = -2.741464025 Simplifying x + -0.125 = -2.741464025 Reorder the terms: -0.125 + x = -2.741464025 Solving -0.125 + x = -2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -2.741464025 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -2.741464025 + 0.125 x = -2.741464025 + 0.125 Combine like terms: -2.741464025 + 0.125 = -2.616464025 x = -2.616464025 Simplifying x = -2.616464025Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.866464025, -2.616464025}
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