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Simplifying -13x2 + -5x + -2x2 + 8 + 9x = 0 Reorder the terms: 8 + -5x + 9x + -13x2 + -2x2 = 0 Combine like terms: -5x + 9x = 4x 8 + 4x + -13x2 + -2x2 = 0 Combine like terms: -13x2 + -2x2 = -15x2 8 + 4x + -15x2 = 0 Solving 8 + 4x + -15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.5333333333 + -0.2666666667x + x2 = 0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + -0.2666666667x + 0.5333333333 + x2 = 0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + -0.2666666667x + x2 = 0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + -0.2666666667x + x2 = 0 + 0.5333333333 -0.2666666667x + x2 = 0 + 0.5333333333 Combine like terms: 0 + 0.5333333333 = 0.5333333333 -0.2666666667x + x2 = 0.5333333333 The x term is -0.2666666667x. Take half its coefficient (-0.1333333334). Square it (0.01777777780) and add it to both sides. Add '0.01777777780' to each side of the equation. -0.2666666667x + 0.01777777780 + x2 = 0.5333333333 + 0.01777777780 Reorder the terms: 0.01777777780 + -0.2666666667x + x2 = 0.5333333333 + 0.01777777780 Combine like terms: 0.5333333333 + 0.01777777780 = 0.5511111111 0.01777777780 + -0.2666666667x + x2 = 0.5511111111 Factor a perfect square on the left side: (x + -0.1333333334)(x + -0.1333333334) = 0.5511111111 Calculate the square root of the right side: 0.742368582 Break this problem into two subproblems by setting (x + -0.1333333334) equal to 0.742368582 and -0.742368582.Subproblem 1
x + -0.1333333334 = 0.742368582 Simplifying x + -0.1333333334 = 0.742368582 Reorder the terms: -0.1333333334 + x = 0.742368582 Solving -0.1333333334 + x = 0.742368582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1333333334' to each side of the equation. -0.1333333334 + 0.1333333334 + x = 0.742368582 + 0.1333333334 Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000 0.0000000000 + x = 0.742368582 + 0.1333333334 x = 0.742368582 + 0.1333333334 Combine like terms: 0.742368582 + 0.1333333334 = 0.8757019154 x = 0.8757019154 Simplifying x = 0.8757019154Subproblem 2
x + -0.1333333334 = -0.742368582 Simplifying x + -0.1333333334 = -0.742368582 Reorder the terms: -0.1333333334 + x = -0.742368582 Solving -0.1333333334 + x = -0.742368582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1333333334' to each side of the equation. -0.1333333334 + 0.1333333334 + x = -0.742368582 + 0.1333333334 Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000 0.0000000000 + x = -0.742368582 + 0.1333333334 x = -0.742368582 + 0.1333333334 Combine like terms: -0.742368582 + 0.1333333334 = -0.6090352486 x = -0.6090352486 Simplifying x = -0.6090352486Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8757019154, -0.6090352486}
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