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Simplifying 8x2 + -10x + 3(6x2 + 3x + -3) = 0 Reorder the terms: 8x2 + -10x + 3(-3 + 3x + 6x2) = 0 8x2 + -10x + (-3 * 3 + 3x * 3 + 6x2 * 3) = 0 8x2 + -10x + (-9 + 9x + 18x2) = 0 Reorder the terms: -9 + -10x + 9x + 8x2 + 18x2 = 0 Combine like terms: -10x + 9x = -1x -9 + -1x + 8x2 + 18x2 = 0 Combine like terms: 8x2 + 18x2 = 26x2 -9 + -1x + 26x2 = 0 Solving -9 + -1x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.3461538462 + -0.03846153846x + x2 = 0 Move the constant term to the right: Add '0.3461538462' to each side of the equation. -0.3461538462 + -0.03846153846x + 0.3461538462 + x2 = 0 + 0.3461538462 Reorder the terms: -0.3461538462 + 0.3461538462 + -0.03846153846x + x2 = 0 + 0.3461538462 Combine like terms: -0.3461538462 + 0.3461538462 = 0.0000000000 0.0000000000 + -0.03846153846x + x2 = 0 + 0.3461538462 -0.03846153846x + x2 = 0 + 0.3461538462 Combine like terms: 0 + 0.3461538462 = 0.3461538462 -0.03846153846x + x2 = 0.3461538462 The x term is -0.03846153846x. Take half its coefficient (-0.01923076923). Square it (0.0003698224852) and add it to both sides. Add '0.0003698224852' to each side of the equation. -0.03846153846x + 0.0003698224852 + x2 = 0.3461538462 + 0.0003698224852 Reorder the terms: 0.0003698224852 + -0.03846153846x + x2 = 0.3461538462 + 0.0003698224852 Combine like terms: 0.3461538462 + 0.0003698224852 = 0.3465236686852 0.0003698224852 + -0.03846153846x + x2 = 0.3465236686852 Factor a perfect square on the left side: (x + -0.01923076923)(x + -0.01923076923) = 0.3465236686852 Calculate the square root of the right side: 0.58866261 Break this problem into two subproblems by setting (x + -0.01923076923) equal to 0.58866261 and -0.58866261.Subproblem 1
x + -0.01923076923 = 0.58866261 Simplifying x + -0.01923076923 = 0.58866261 Reorder the terms: -0.01923076923 + x = 0.58866261 Solving -0.01923076923 + x = 0.58866261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01923076923' to each side of the equation. -0.01923076923 + 0.01923076923 + x = 0.58866261 + 0.01923076923 Combine like terms: -0.01923076923 + 0.01923076923 = 0.00000000000 0.00000000000 + x = 0.58866261 + 0.01923076923 x = 0.58866261 + 0.01923076923 Combine like terms: 0.58866261 + 0.01923076923 = 0.60789337923 x = 0.60789337923 Simplifying x = 0.60789337923Subproblem 2
x + -0.01923076923 = -0.58866261 Simplifying x + -0.01923076923 = -0.58866261 Reorder the terms: -0.01923076923 + x = -0.58866261 Solving -0.01923076923 + x = -0.58866261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01923076923' to each side of the equation. -0.01923076923 + 0.01923076923 + x = -0.58866261 + 0.01923076923 Combine like terms: -0.01923076923 + 0.01923076923 = 0.00000000000 0.00000000000 + x = -0.58866261 + 0.01923076923 x = -0.58866261 + 0.01923076923 Combine like terms: -0.58866261 + 0.01923076923 = -0.56943184077 x = -0.56943184077 Simplifying x = -0.56943184077Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.60789337923, -0.56943184077}
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