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Simplifying (-2x2 + 6x + 1) + -2(4x2 + -3x + 1) = 0 Reorder the terms: (1 + 6x + -2x2) + -2(4x2 + -3x + 1) = 0 Remove parenthesis around (1 + 6x + -2x2) 1 + 6x + -2x2 + -2(4x2 + -3x + 1) = 0 Reorder the terms: 1 + 6x + -2x2 + -2(1 + -3x + 4x2) = 0 1 + 6x + -2x2 + (1 * -2 + -3x * -2 + 4x2 * -2) = 0 1 + 6x + -2x2 + (-2 + 6x + -8x2) = 0 Reorder the terms: 1 + -2 + 6x + 6x + -2x2 + -8x2 = 0 Combine like terms: 1 + -2 = -1 -1 + 6x + 6x + -2x2 + -8x2 = 0 Combine like terms: 6x + 6x = 12x -1 + 12x + -2x2 + -8x2 = 0 Combine like terms: -2x2 + -8x2 = -10x2 -1 + 12x + -10x2 = 0 Solving -1 + 12x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 0.1 + -1.2x + x2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + -1.2x + -0.1 + x2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + -1.2x + x2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + -1.2x + x2 = 0.0 + -0.1 -1.2x + x2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 -1.2x + x2 = -0.1 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -0.1 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.1 + 0.36 Combine like terms: -0.1 + 0.36 = 0.26 0.36 + -1.2x + x2 = 0.26 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.26 Calculate the square root of the right side: 0.509901951 Break this problem into two subproblems by setting (x + -0.6) equal to 0.509901951 and -0.509901951.Subproblem 1
x + -0.6 = 0.509901951 Simplifying x + -0.6 = 0.509901951 Reorder the terms: -0.6 + x = 0.509901951 Solving -0.6 + x = 0.509901951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.509901951 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.509901951 + 0.6 x = 0.509901951 + 0.6 Combine like terms: 0.509901951 + 0.6 = 1.109901951 x = 1.109901951 Simplifying x = 1.109901951Subproblem 2
x + -0.6 = -0.509901951 Simplifying x + -0.6 = -0.509901951 Reorder the terms: -0.6 + x = -0.509901951 Solving -0.6 + x = -0.509901951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.509901951 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.509901951 + 0.6 x = -0.509901951 + 0.6 Combine like terms: -0.509901951 + 0.6 = 0.090098049 x = 0.090098049 Simplifying x = 0.090098049Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.109901951, 0.090098049}
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