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Simplifying 7x2 + 6x + -10 = 0 Reorder the terms: -10 + 6x + 7x2 = 0 Solving -10 + 6x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 0.8571428571x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 0.8571428571x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 0.8571428571x + x2 = 0 + 1.428571429 0.8571428571x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 0.8571428571x + x2 = 1.428571429 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = 1.428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 1.428571429 + 0.1836734694 Combine like terms: 1.428571429 + 0.1836734694 = 1.6122448984 0.1836734694 + 0.8571428571x + x2 = 1.6122448984 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 1.6122448984 Calculate the square root of the right side: 1.26974206 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 1.26974206 and -1.26974206.Subproblem 1
x + 0.4285714286 = 1.26974206 Simplifying x + 0.4285714286 = 1.26974206 Reorder the terms: 0.4285714286 + x = 1.26974206 Solving 0.4285714286 + x = 1.26974206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 1.26974206 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 1.26974206 + -0.4285714286 x = 1.26974206 + -0.4285714286 Combine like terms: 1.26974206 + -0.4285714286 = 0.8411706314 x = 0.8411706314 Simplifying x = 0.8411706314Subproblem 2
x + 0.4285714286 = -1.26974206 Simplifying x + 0.4285714286 = -1.26974206 Reorder the terms: 0.4285714286 + x = -1.26974206 Solving 0.4285714286 + x = -1.26974206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -1.26974206 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -1.26974206 + -0.4285714286 x = -1.26974206 + -0.4285714286 Combine like terms: -1.26974206 + -0.4285714286 = -1.6983134886 x = -1.6983134886 Simplifying x = -1.6983134886Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8411706314, -1.6983134886}
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