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Simplifying (4x2 + -1x + 5) + -1(9x2 + -4x + 1) = 0 Reorder the terms: (5 + -1x + 4x2) + -1(9x2 + -4x + 1) = 0 Remove parenthesis around (5 + -1x + 4x2) 5 + -1x + 4x2 + -1(9x2 + -4x + 1) = 0 Reorder the terms: 5 + -1x + 4x2 + -1(1 + -4x + 9x2) = 0 5 + -1x + 4x2 + (1 * -1 + -4x * -1 + 9x2 * -1) = 0 5 + -1x + 4x2 + (-1 + 4x + -9x2) = 0 Reorder the terms: 5 + -1 + -1x + 4x + 4x2 + -9x2 = 0 Combine like terms: 5 + -1 = 4 4 + -1x + 4x + 4x2 + -9x2 = 0 Combine like terms: -1x + 4x = 3x 4 + 3x + 4x2 + -9x2 = 0 Combine like terms: 4x2 + -9x2 = -5x2 4 + 3x + -5x2 = 0 Solving 4 + 3x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + -0.6x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.6x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.6x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.6x + x2 = 0 + 0.8 -0.6x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.6x + x2 = 0.8 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.8 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.8 + 0.09 Combine like terms: 0.8 + 0.09 = 0.89 0.09 + -0.6x + x2 = 0.89 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + -0.3) equal to 0.943398113 and -0.943398113.Subproblem 1
x + -0.3 = 0.943398113 Simplifying x + -0.3 = 0.943398113 Reorder the terms: -0.3 + x = 0.943398113 Solving -0.3 + x = 0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.943398113 + 0.3 x = 0.943398113 + 0.3 Combine like terms: 0.943398113 + 0.3 = 1.243398113 x = 1.243398113 Simplifying x = 1.243398113Subproblem 2
x + -0.3 = -0.943398113 Simplifying x + -0.3 = -0.943398113 Reorder the terms: -0.3 + x = -0.943398113 Solving -0.3 + x = -0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.943398113 + 0.3 x = -0.943398113 + 0.3 Combine like terms: -0.943398113 + 0.3 = -0.643398113 x = -0.643398113 Simplifying x = -0.643398113Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.243398113, -0.643398113}
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