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Simplifying 7x2 + 26x + 15 = (x + 5) Reorder the terms: 15 + 26x + 7x2 = (x + 5) Reorder the terms: 15 + 26x + 7x2 = (5 + x) Remove parenthesis around (5 + x) 15 + 26x + 7x2 = 5 + x Solving 15 + 26x + 7x2 = 5 + x Solving for variable 'x'. Reorder the terms: 15 + -5 + 26x + -1x + 7x2 = 5 + x + -5 + -1x Combine like terms: 15 + -5 = 10 10 + 26x + -1x + 7x2 = 5 + x + -5 + -1x Combine like terms: 26x + -1x = 25x 10 + 25x + 7x2 = 5 + x + -5 + -1x Reorder the terms: 10 + 25x + 7x2 = 5 + -5 + x + -1x Combine like terms: 5 + -5 = 0 10 + 25x + 7x2 = 0 + x + -1x 10 + 25x + 7x2 = x + -1x Combine like terms: x + -1x = 0 10 + 25x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.428571429 + 3.571428571x + x2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + 3.571428571x + -1.428571429 + x2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + 3.571428571x + x2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + 3.571428571x + x2 = 0 + -1.428571429 3.571428571x + x2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 3.571428571x + x2 = -1.428571429 The x term is 3.571428571x. Take half its coefficient (1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. 3.571428571x + 3.188775511 + x2 = -1.428571429 + 3.188775511 Reorder the terms: 3.188775511 + 3.571428571x + x2 = -1.428571429 + 3.188775511 Combine like terms: -1.428571429 + 3.188775511 = 1.760204082 3.188775511 + 3.571428571x + x2 = 1.760204082 Factor a perfect square on the left side: (x + 1.785714286)(x + 1.785714286) = 1.760204082 Calculate the square root of the right side: 1.32672683 Break this problem into two subproblems by setting (x + 1.785714286) equal to 1.32672683 and -1.32672683.Subproblem 1
x + 1.785714286 = 1.32672683 Simplifying x + 1.785714286 = 1.32672683 Reorder the terms: 1.785714286 + x = 1.32672683 Solving 1.785714286 + x = 1.32672683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = 1.32672683 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = 1.32672683 + -1.785714286 x = 1.32672683 + -1.785714286 Combine like terms: 1.32672683 + -1.785714286 = -0.458987456 x = -0.458987456 Simplifying x = -0.458987456Subproblem 2
x + 1.785714286 = -1.32672683 Simplifying x + 1.785714286 = -1.32672683 Reorder the terms: 1.785714286 + x = -1.32672683 Solving 1.785714286 + x = -1.32672683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = -1.32672683 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = -1.32672683 + -1.785714286 x = -1.32672683 + -1.785714286 Combine like terms: -1.32672683 + -1.785714286 = -3.112441116 x = -3.112441116 Simplifying x = -3.112441116Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.458987456, -3.112441116}
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