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Simplifying 7x2 + 6x = 24 Reorder the terms: 6x + 7x2 = 24 Solving 6x + 7x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 6x + 7x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.428571429 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + 0.8571428571x + 3.428571429 + x2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + 0.8571428571x + x2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + 0.8571428571x + x2 = 0 + 3.428571429 0.8571428571x + x2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 0.8571428571x + x2 = 3.428571429 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 = 3.428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 3.428571429 + 0.1836734694 Combine like terms: 3.428571429 + 0.1836734694 = 3.6122448984 0.1836734694 + 0.8571428571x + x2 = 3.6122448984 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 3.6122448984 Calculate the square root of the right side: 1.900590671 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 1.900590671 and -1.900590671.Subproblem 1
x + 0.4285714286 = 1.900590671 Simplifying x + 0.4285714286 = 1.900590671 Reorder the terms: 0.4285714286 + x = 1.900590671 Solving 0.4285714286 + x = 1.900590671 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 = 1.900590671 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 1.900590671 + -0.4285714286 x = 1.900590671 + -0.4285714286 Combine like terms: 1.900590671 + -0.4285714286 = 1.4720192424 x = 1.4720192424 Simplifying x = 1.4720192424Subproblem 2
x + 0.4285714286 = -1.900590671 Simplifying x + 0.4285714286 = -1.900590671 Reorder the terms: 0.4285714286 + x = -1.900590671 Solving 0.4285714286 + x = -1.900590671 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 = -1.900590671 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -1.900590671 + -0.4285714286 x = -1.900590671 + -0.4285714286 Combine like terms: -1.900590671 + -0.4285714286 = -2.3291620996 x = -2.3291620996 Simplifying x = -2.3291620996Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4720192424, -2.3291620996}
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