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Simplifying 4x2 + -5(4x) + 3 = 0 Remove parenthesis around (4x) 4x2 + -5 * 4x + 3 = 0 Multiply -5 * 4 4x2 + -20x + 3 = 0 Reorder the terms: 3 + -20x + 4x2 = 0 Solving 3 + -20x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -5x + x2 = 0 + -0.75 -5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -5x + x2 = -0.75 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.75 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.75 + 6.25 Combine like terms: -0.75 + 6.25 = 5.5 6.25 + -5x + x2 = 5.5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + -2.5) equal to 2.34520788 and -2.34520788.Subproblem 1
x + -2.5 = 2.34520788 Simplifying x + -2.5 = 2.34520788 Reorder the terms: -2.5 + x = 2.34520788 Solving -2.5 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.34520788 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.34520788 + 2.5 x = 2.34520788 + 2.5 Combine like terms: 2.34520788 + 2.5 = 4.84520788 x = 4.84520788 Simplifying x = 4.84520788Subproblem 2
x + -2.5 = -2.34520788 Simplifying x + -2.5 = -2.34520788 Reorder the terms: -2.5 + x = -2.34520788 Solving -2.5 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.34520788 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.34520788 + 2.5 x = -2.34520788 + 2.5 Combine like terms: -2.34520788 + 2.5 = 0.15479212 x = 0.15479212 Simplifying x = 0.15479212Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.84520788, 0.15479212}
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