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Simplifying 4x2 + 12x = 2.75 Reorder the terms: 12x + 4x2 = 2.75 Solving 12x + 4x2 = 2.75 Solving for variable 'x'. Reorder the terms: -2.75 + 12x + 4x2 = 2.75 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 -2.75 + 12x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.6875 + 3x + x2 = 0.00 Move the constant term to the right: Add '0.6875' to each side of the equation. -0.6875 + 3x + 0.6875 + x2 = 0.00 + 0.6875 Reorder the terms: -0.6875 + 0.6875 + 3x + x2 = 0.00 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + 3x + x2 = 0.00 + 0.6875 3x + x2 = 0.00 + 0.6875 Combine like terms: 0.00 + 0.6875 = 0.6875 3x + x2 = 0.6875 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 = 0.6875 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.6875 + 2.25 Combine like terms: 0.6875 + 2.25 = 2.9375 2.25 + 3x + x2 = 2.9375 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.9375 Calculate the square root of the right side: 1.71391365 Break this problem into two subproblems by setting (x + 1.5) equal to 1.71391365 and -1.71391365.Subproblem 1
x + 1.5 = 1.71391365 Simplifying x + 1.5 = 1.71391365 Reorder the terms: 1.5 + x = 1.71391365 Solving 1.5 + x = 1.71391365 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 = 1.71391365 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.71391365 + -1.5 x = 1.71391365 + -1.5 Combine like terms: 1.71391365 + -1.5 = 0.21391365 x = 0.21391365 Simplifying x = 0.21391365Subproblem 2
x + 1.5 = -1.71391365 Simplifying x + 1.5 = -1.71391365 Reorder the terms: 1.5 + x = -1.71391365 Solving 1.5 + x = -1.71391365 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 = -1.71391365 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.71391365 + -1.5 x = -1.71391365 + -1.5 Combine like terms: -1.71391365 + -1.5 = -3.21391365 x = -3.21391365 Simplifying x = -3.21391365Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.21391365, -3.21391365}
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