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Simplifying 4x2 + x = 15 Reorder the terms: x + 4x2 = 15 Solving x + 4x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + x + 4x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 0.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 0.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 0.25x + x2 = 0 + 3.75 0.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 0.25x + x2 = 3.75 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. 0.25x + 0.25 + x2 = 3.75 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 3.75 + 0.25 Combine like terms: 3.75 + 0.25 = 4 0.25 + 0.25x + x2 = 4 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + 0.5) equal to 2 and -2.Subproblem 1
x + 0.5 = 2 Simplifying x + 0.5 = 2 Reorder the terms: 0.5 + x = 2 Solving 0.5 + x = 2 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 = 2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2 + -0.5 x = 2 + -0.5 Combine like terms: 2 + -0.5 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + 0.5 = -2 Simplifying x + 0.5 = -2 Reorder the terms: 0.5 + x = -2 Solving 0.5 + x = -2 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 = -2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2 + -0.5 x = -2 + -0.5 Combine like terms: -2 + -0.5 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, -2.5}
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