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Simplifying 10x2 + -7x + -13 = 0 Reorder the terms: -13 + -7x + 10x2 = 0 Solving -13 + -7x + 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 + -0.7x + x2 = 0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + -0.7x + 1.3 + x2 = 0 + 1.3 Reorder the terms: -1.3 + 1.3 + -0.7x + x2 = 0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + -0.7x + x2 = 0 + 1.3 -0.7x + x2 = 0 + 1.3 Combine like terms: 0 + 1.3 = 1.3 -0.7x + x2 = 1.3 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = 1.3 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 1.3 + 0.1225 Combine like terms: 1.3 + 0.1225 = 1.4225 0.1225 + -0.7x + x2 = 1.4225 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 1.4225 Calculate the square root of the right side: 1.192686044 Break this problem into two subproblems by setting (x + -0.35) equal to 1.192686044 and -1.192686044.Subproblem 1
x + -0.35 = 1.192686044 Simplifying x + -0.35 = 1.192686044 Reorder the terms: -0.35 + x = 1.192686044 Solving -0.35 + x = 1.192686044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 1.192686044 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 1.192686044 + 0.35 x = 1.192686044 + 0.35 Combine like terms: 1.192686044 + 0.35 = 1.542686044 x = 1.542686044 Simplifying x = 1.542686044Subproblem 2
x + -0.35 = -1.192686044 Simplifying x + -0.35 = -1.192686044 Reorder the terms: -0.35 + x = -1.192686044 Solving -0.35 + x = -1.192686044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -1.192686044 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -1.192686044 + 0.35 x = -1.192686044 + 0.35 Combine like terms: -1.192686044 + 0.35 = -0.842686044 x = -0.842686044 Simplifying x = -0.842686044Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.542686044, -0.842686044}
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