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Simplifying 10x2 + -6x + -13 = 0 Reorder the terms: -13 + -6x + 10x2 = 0 Solving -13 + -6x + 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'. -1.3 + -0.6x + x2 = 0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + -0.6x + 1.3 + x2 = 0 + 1.3 Reorder the terms: -1.3 + 1.3 + -0.6x + x2 = 0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + -0.6x + x2 = 0 + 1.3 -0.6x + x2 = 0 + 1.3 Combine like terms: 0 + 1.3 = 1.3 -0.6x + x2 = 1.3 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 = 1.3 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1.3 + 0.09 Combine like terms: 1.3 + 0.09 = 1.39 0.09 + -0.6x + x2 = 1.39 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.39 Calculate the square root of the right side: 1.178982612 Break this problem into two subproblems by setting (x + -0.3) equal to 1.178982612 and -1.178982612.Subproblem 1
x + -0.3 = 1.178982612 Simplifying x + -0.3 = 1.178982612 Reorder the terms: -0.3 + x = 1.178982612 Solving -0.3 + x = 1.178982612 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 = 1.178982612 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.178982612 + 0.3 x = 1.178982612 + 0.3 Combine like terms: 1.178982612 + 0.3 = 1.478982612 x = 1.478982612 Simplifying x = 1.478982612Subproblem 2
x + -0.3 = -1.178982612 Simplifying x + -0.3 = -1.178982612 Reorder the terms: -0.3 + x = -1.178982612 Solving -0.3 + x = -1.178982612 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 = -1.178982612 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.178982612 + 0.3 x = -1.178982612 + 0.3 Combine like terms: -1.178982612 + 0.3 = -0.878982612 x = -0.878982612 Simplifying x = -0.878982612Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.478982612, -0.878982612}
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