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Simplifying (4x + 6) + -1(9x2 + -13x) = 0 Reorder the terms: (6 + 4x) + -1(9x2 + -13x) = 0 Remove parenthesis around (6 + 4x) 6 + 4x + -1(9x2 + -13x) = 0 Reorder the terms: 6 + 4x + -1(-13x + 9x2) = 0 6 + 4x + (-13x * -1 + 9x2 * -1) = 0 6 + 4x + (13x + -9x2) = 0 Combine like terms: 4x + 13x = 17x 6 + 17x + -9x2 = 0 Solving 6 + 17x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.6666666667 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1.888888889x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1.888888889x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1.888888889x + x2 = 0 + 0.6666666667 -1.888888889x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1.888888889x + x2 = 0.6666666667 The x term is -1.888888889x. Take half its coefficient (-0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. -1.888888889x + 0.8919753087 + x2 = 0.6666666667 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 0.6666666667 + 0.8919753087 Combine like terms: 0.6666666667 + 0.8919753087 = 1.5586419754 0.8919753087 + -1.888888889x + x2 = 1.5586419754 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 1.5586419754 Calculate the square root of the right side: 1.248455836 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 1.248455836 and -1.248455836.Subproblem 1
x + -0.9444444445 = 1.248455836 Simplifying x + -0.9444444445 = 1.248455836 Reorder the terms: -0.9444444445 + x = 1.248455836 Solving -0.9444444445 + x = 1.248455836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = 1.248455836 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 1.248455836 + 0.9444444445 x = 1.248455836 + 0.9444444445 Combine like terms: 1.248455836 + 0.9444444445 = 2.1929002805 x = 2.1929002805 Simplifying x = 2.1929002805Subproblem 2
x + -0.9444444445 = -1.248455836 Simplifying x + -0.9444444445 = -1.248455836 Reorder the terms: -0.9444444445 + x = -1.248455836 Solving -0.9444444445 + x = -1.248455836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = -1.248455836 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -1.248455836 + 0.9444444445 x = -1.248455836 + 0.9444444445 Combine like terms: -1.248455836 + 0.9444444445 = -0.3040113915 x = -0.3040113915 Simplifying x = -0.3040113915Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1929002805, -0.3040113915}
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