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Simplifying 10x2 + -4 + 3x + -7x2 + -13 = 0 Reorder the terms: -4 + -13 + 3x + 10x2 + -7x2 = 0 Combine like terms: -4 + -13 = -17 -17 + 3x + 10x2 + -7x2 = 0 Combine like terms: 10x2 + -7x2 = 3x2 -17 + 3x + 3x2 = 0 Solving -17 + 3x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.666666667 + x + x2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + x + 5.666666667 + x2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + x + x2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + x + x2 = 0 + 5.666666667 x + x2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 x + x2 = 5.666666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 5.666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 5.666666667 + 0.25 Combine like terms: 5.666666667 + 0.25 = 5.916666667 1.25 + x2 = 5.916666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.916666667 Calculate the square root of the right side: 2.43241992 Break this problem into two subproblems by setting (x + 0.5) equal to 2.43241992 and -2.43241992.Subproblem 1
x + 0.5 = 2.43241992 Simplifying x + 0.5 = 2.43241992 Reorder the terms: 0.5 + x = 2.43241992 Solving 0.5 + x = 2.43241992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.43241992 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.43241992 + -0.5 x = 2.43241992 + -0.5 Combine like terms: 2.43241992 + -0.5 = 1.93241992 x = 1.93241992 Simplifying x = 1.93241992Subproblem 2
x + 0.5 = -2.43241992 Simplifying x + 0.5 = -2.43241992 Reorder the terms: 0.5 + x = -2.43241992 Solving 0.5 + x = -2.43241992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.43241992 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.43241992 + -0.5 x = -2.43241992 + -0.5 Combine like terms: -2.43241992 + -0.5 = -2.93241992 x = -2.93241992 Simplifying x = -2.93241992Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.93241992, -2.93241992}
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