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Simplifying 5x2 + -6x = 4x2 + 6x + -3 Reorder the terms: -6x + 5x2 = 4x2 + 6x + -3 Reorder the terms: -6x + 5x2 = -3 + 6x + 4x2 Solving -6x + 5x2 = -3 + 6x + 4x2 Solving for variable 'x'. Reorder the terms: 3 + -6x + -6x + 5x2 + -4x2 = -3 + 6x + 4x2 + 3 + -6x + -4x2 Combine like terms: -6x + -6x = -12x 3 + -12x + 5x2 + -4x2 = -3 + 6x + 4x2 + 3 + -6x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 3 + -12x + 1x2 = -3 + 6x + 4x2 + 3 + -6x + -4x2 Reorder the terms: 3 + -12x + 1x2 = -3 + 3 + 6x + -6x + 4x2 + -4x2 Combine like terms: -3 + 3 = 0 3 + -12x + 1x2 = 0 + 6x + -6x + 4x2 + -4x2 3 + -12x + 1x2 = 6x + -6x + 4x2 + -4x2 Combine like terms: 6x + -6x = 0 3 + -12x + 1x2 = 0 + 4x2 + -4x2 3 + -12x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 3 + -12x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -12x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -12x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -12x + x2 = 0 + -3 -12x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -12x + x2 = -3 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -3 + 36 Reorder the terms: 36 + -12x + x2 = -3 + 36 Combine like terms: -3 + 36 = 33 36 + -12x + x2 = 33 Factor a perfect square on the left side: (x + -6)(x + -6) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + -6) equal to 5.744562647 and -5.744562647.Subproblem 1
x + -6 = 5.744562647 Simplifying x + -6 = 5.744562647 Reorder the terms: -6 + x = 5.744562647 Solving -6 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.744562647 + 6 x = 5.744562647 + 6 Combine like terms: 5.744562647 + 6 = 11.744562647 x = 11.744562647 Simplifying x = 11.744562647Subproblem 2
x + -6 = -5.744562647 Simplifying x + -6 = -5.744562647 Reorder the terms: -6 + x = -5.744562647 Solving -6 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.744562647 + 6 x = -5.744562647 + 6 Combine like terms: -5.744562647 + 6 = 0.255437353 x = 0.255437353 Simplifying x = 0.255437353Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.744562647, 0.255437353}
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