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Simplifying 3x(-5x + -5) + -6(5 + 7x) = 0 Reorder the terms: 3x(-5 + -5x) + -6(5 + 7x) = 0 (-5 * 3x + -5x * 3x) + -6(5 + 7x) = 0 (-15x + -15x2) + -6(5 + 7x) = 0 -15x + -15x2 + (5 * -6 + 7x * -6) = 0 -15x + -15x2 + (-30 + -42x) = 0 Reorder the terms: -30 + -15x + -42x + -15x2 = 0 Combine like terms: -15x + -42x = -57x -30 + -57x + -15x2 = 0 Solving -30 + -57x + -15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-3'. -3(10 + 19x + 5x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(10 + 19x + 5x2)' equal to zero and attempt to solve: Simplifying 10 + 19x + 5x2 = 0 Solving 10 + 19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 3.8x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.8x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.8x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.8x + x2 = 0 + -2 3.8x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.8x + x2 = -2 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = -2 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = -2 + 3.61 Combine like terms: -2 + 3.61 = 1.61 3.61 + 3.8x + x2 = 1.61 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (x + 1.9) equal to 1.268857754 and -1.268857754.Subproblem 1
x + 1.9 = 1.268857754 Simplifying x + 1.9 = 1.268857754 Reorder the terms: 1.9 + x = 1.268857754 Solving 1.9 + x = 1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 1.268857754 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 1.268857754 + -1.9 x = 1.268857754 + -1.9 Combine like terms: 1.268857754 + -1.9 = -0.631142246 x = -0.631142246 Simplifying x = -0.631142246Subproblem 2
x + 1.9 = -1.268857754 Simplifying x + 1.9 = -1.268857754 Reorder the terms: 1.9 + x = -1.268857754 Solving 1.9 + x = -1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -1.268857754 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -1.268857754 + -1.9 x = -1.268857754 + -1.9 Combine like terms: -1.268857754 + -1.9 = -3.168857754 x = -3.168857754 Simplifying x = -3.168857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.631142246, -3.168857754}Solution
x = {-0.631142246, -3.168857754}
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