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Simplifying 0 = 6x2 + 10x + -3 Reorder the terms: 0 = -3 + 10x + 6x2 Solving 0 = -3 + 10x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 3 = 3 3 + -10x + -6x2 = -3 + 10x + 6x2 + 3 + -10x + -6x2 Reorder the terms: 3 + -10x + -6x2 = -3 + 3 + 10x + -10x + 6x2 + -6x2 Combine like terms: -3 + 3 = 0 3 + -10x + -6x2 = 0 + 10x + -10x + 6x2 + -6x2 3 + -10x + -6x2 = 10x + -10x + 6x2 + -6x2 Combine like terms: 10x + -10x = 0 3 + -10x + -6x2 = 0 + 6x2 + -6x2 3 + -10x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 3 + -10x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.5 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.666666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.666666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.666666667x + x2 = 0 + 0.5 1.666666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.666666667x + x2 = 0.5 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 0.5 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 0.5 + 0.6944444447 Combine like terms: 0.5 + 0.6944444447 = 1.1944444447 0.6944444447 + 1.666666667x + x2 = 1.1944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 1.1944444447 Calculate the square root of the right side: 1.092906421 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.092906421 and -1.092906421.Subproblem 1
x + 0.8333333335 = 1.092906421 Simplifying x + 0.8333333335 = 1.092906421 Reorder the terms: 0.8333333335 + x = 1.092906421 Solving 0.8333333335 + x = 1.092906421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.092906421 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.092906421 + -0.8333333335 x = 1.092906421 + -0.8333333335 Combine like terms: 1.092906421 + -0.8333333335 = 0.2595730875 x = 0.2595730875 Simplifying x = 0.2595730875Subproblem 2
x + 0.8333333335 = -1.092906421 Simplifying x + 0.8333333335 = -1.092906421 Reorder the terms: 0.8333333335 + x = -1.092906421 Solving 0.8333333335 + x = -1.092906421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.092906421 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.092906421 + -0.8333333335 x = -1.092906421 + -0.8333333335 Combine like terms: -1.092906421 + -0.8333333335 = -1.9262397545 x = -1.9262397545 Simplifying x = -1.9262397545Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2595730875, -1.9262397545}
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