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Simplifying 4x2 + 6x + -3 = 46 Reorder the terms: -3 + 6x + 4x2 = 46 Solving -3 + 6x + 4x2 = 46 Solving for variable 'x'. Reorder the terms: -3 + -46 + 6x + 4x2 = 46 + -46 Combine like terms: -3 + -46 = -49 -49 + 6x + 4x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -49 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + 1.5x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + 1.5x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + 1.5x + x2 = 0 + 12.25 1.5x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 1.5x + x2 = 12.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 12.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 12.25 + 0.5625 Combine like terms: 12.25 + 0.5625 = 12.8125 0.5625 + 1.5x + x2 = 12.8125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 12.8125 Calculate the square root of the right side: 3.579455266 Break this problem into two subproblems by setting (x + 0.75) equal to 3.579455266 and -3.579455266.Subproblem 1
x + 0.75 = 3.579455266 Simplifying x + 0.75 = 3.579455266 Reorder the terms: 0.75 + x = 3.579455266 Solving 0.75 + x = 3.579455266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 3.579455266 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.579455266 + -0.75 x = 3.579455266 + -0.75 Combine like terms: 3.579455266 + -0.75 = 2.829455266 x = 2.829455266 Simplifying x = 2.829455266Subproblem 2
x + 0.75 = -3.579455266 Simplifying x + 0.75 = -3.579455266 Reorder the terms: 0.75 + x = -3.579455266 Solving 0.75 + x = -3.579455266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -3.579455266 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.579455266 + -0.75 x = -3.579455266 + -0.75 Combine like terms: -3.579455266 + -0.75 = -4.329455266 x = -4.329455266 Simplifying x = -4.329455266Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.829455266, -4.329455266}
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