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Simplifying 10x2 + -13x + -6 = 0 Reorder the terms: -6 + -13x + 10x2 = 0 Solving -6 + -13x + 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'. -0.6 + -1.3x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.3x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.3x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.3x + x2 = 0 + 0.6 -1.3x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.3x + x2 = 0.6 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = 0.6 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = 0.6 + 0.4225 Combine like terms: 0.6 + 0.4225 = 1.0225 0.4225 + -1.3x + x2 = 1.0225 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = 1.0225 Calculate the square root of the right side: 1.011187421 Break this problem into two subproblems by setting (x + -0.65) equal to 1.011187421 and -1.011187421.Subproblem 1
x + -0.65 = 1.011187421 Simplifying x + -0.65 = 1.011187421 Reorder the terms: -0.65 + x = 1.011187421 Solving -0.65 + x = 1.011187421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = 1.011187421 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 1.011187421 + 0.65 x = 1.011187421 + 0.65 Combine like terms: 1.011187421 + 0.65 = 1.661187421 x = 1.661187421 Simplifying x = 1.661187421Subproblem 2
x + -0.65 = -1.011187421 Simplifying x + -0.65 = -1.011187421 Reorder the terms: -0.65 + x = -1.011187421 Solving -0.65 + x = -1.011187421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = -1.011187421 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -1.011187421 + 0.65 x = -1.011187421 + 0.65 Combine like terms: -1.011187421 + 0.65 = -0.361187421 x = -0.361187421 Simplifying x = -0.361187421Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.661187421, -0.361187421}
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