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Simplifying 2x2 + 6x = 5.625 Reorder the terms: 6x + 2x2 = 5.625 Solving 6x + 2x2 = 5.625 Solving for variable 'x'. Reorder the terms: -5.625 + 6x + 2x2 = 5.625 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 -5.625 + 6x + 2x2 = 0.000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.8125 + 3x + x2 = 0.000 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + 3x + 2.8125 + x2 = 0.000 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + 3x + x2 = 0.000 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + 3x + x2 = 0.000 + 2.8125 3x + x2 = 0.000 + 2.8125 Combine like terms: 0.000 + 2.8125 = 2.8125 3x + x2 = 2.8125 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2.8125 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2.8125 + 2.25 Combine like terms: 2.8125 + 2.25 = 5.0625 2.25 + 3x + x2 = 5.0625 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + 1.5) equal to 2.25 and -2.25.Subproblem 1
x + 1.5 = 2.25 Simplifying x + 1.5 = 2.25 Reorder the terms: 1.5 + x = 2.25 Solving 1.5 + x = 2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.25 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.25 + -1.5 x = 2.25 + -1.5 Combine like terms: 2.25 + -1.5 = 0.75 x = 0.75 Simplifying x = 0.75Subproblem 2
x + 1.5 = -2.25 Simplifying x + 1.5 = -2.25 Reorder the terms: 1.5 + x = -2.25 Solving 1.5 + x = -2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.25 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.25 + -1.5 x = -2.25 + -1.5 Combine like terms: -2.25 + -1.5 = -3.75 x = -3.75 Simplifying x = -3.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.75, -3.75}
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