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Simplifying 4x(6x + -5) + -5(3 + -5x) = 0 Reorder the terms: 4x(-5 + 6x) + -5(3 + -5x) = 0 (-5 * 4x + 6x * 4x) + -5(3 + -5x) = 0 (-20x + 24x2) + -5(3 + -5x) = 0 -20x + 24x2 + (3 * -5 + -5x * -5) = 0 -20x + 24x2 + (-15 + 25x) = 0 Reorder the terms: -15 + -20x + 25x + 24x2 = 0 Combine like terms: -20x + 25x = 5x -15 + 5x + 24x2 = 0 Solving -15 + 5x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.625 + 0.2083333333x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.2083333333x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.2083333333x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.2083333333x + x2 = 0 + 0.625 0.2083333333x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.2083333333x + x2 = 0.625 The x term is 0.2083333333x. Take half its coefficient (0.1041666667). Square it (0.01085069445) and add it to both sides. Add '0.01085069445' to each side of the equation. 0.2083333333x + 0.01085069445 + x2 = 0.625 + 0.01085069445 Reorder the terms: 0.01085069445 + 0.2083333333x + x2 = 0.625 + 0.01085069445 Combine like terms: 0.625 + 0.01085069445 = 0.63585069445 0.01085069445 + 0.2083333333x + x2 = 0.63585069445 Factor a perfect square on the left side: (x + 0.1041666667)(x + 0.1041666667) = 0.63585069445 Calculate the square root of the right side: 0.797402467 Break this problem into two subproblems by setting (x + 0.1041666667) equal to 0.797402467 and -0.797402467.Subproblem 1
x + 0.1041666667 = 0.797402467 Simplifying x + 0.1041666667 = 0.797402467 Reorder the terms: 0.1041666667 + x = 0.797402467 Solving 0.1041666667 + x = 0.797402467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1041666667' to each side of the equation. 0.1041666667 + -0.1041666667 + x = 0.797402467 + -0.1041666667 Combine like terms: 0.1041666667 + -0.1041666667 = 0.0000000000 0.0000000000 + x = 0.797402467 + -0.1041666667 x = 0.797402467 + -0.1041666667 Combine like terms: 0.797402467 + -0.1041666667 = 0.6932358003 x = 0.6932358003 Simplifying x = 0.6932358003Subproblem 2
x + 0.1041666667 = -0.797402467 Simplifying x + 0.1041666667 = -0.797402467 Reorder the terms: 0.1041666667 + x = -0.797402467 Solving 0.1041666667 + x = -0.797402467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1041666667' to each side of the equation. 0.1041666667 + -0.1041666667 + x = -0.797402467 + -0.1041666667 Combine like terms: 0.1041666667 + -0.1041666667 = 0.0000000000 0.0000000000 + x = -0.797402467 + -0.1041666667 x = -0.797402467 + -0.1041666667 Combine like terms: -0.797402467 + -0.1041666667 = -0.9015691337 x = -0.9015691337 Simplifying x = -0.9015691337Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6932358003, -0.9015691337}
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