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Simplifying 7x2 = -26x + 15 Reorder the terms: 7x2 = 15 + -26x Solving 7x2 = 15 + -26x Solving for variable 'x'. Reorder the terms: -15 + 26x + 7x2 = 15 + -26x + -15 + 26x Reorder the terms: -15 + 26x + 7x2 = 15 + -15 + -26x + 26x Combine like terms: 15 + -15 = 0 -15 + 26x + 7x2 = 0 + -26x + 26x -15 + 26x + 7x2 = -26x + 26x Combine like terms: -26x + 26x = 0 -15 + 26x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.142857143 + 3.714285714x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + 3.714285714x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + 3.714285714x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + 3.714285714x + x2 = 0 + 2.142857143 3.714285714x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 3.714285714x + x2 = 2.142857143 The x term is 3.714285714x. Take half its coefficient (1.857142857). Square it (3.448979591) and add it to both sides. Add '3.448979591' to each side of the equation. 3.714285714x + 3.448979591 + x2 = 2.142857143 + 3.448979591 Reorder the terms: 3.448979591 + 3.714285714x + x2 = 2.142857143 + 3.448979591 Combine like terms: 2.142857143 + 3.448979591 = 5.591836734 3.448979591 + 3.714285714x + x2 = 5.591836734 Factor a perfect square on the left side: (x + 1.857142857)(x + 1.857142857) = 5.591836734 Calculate the square root of the right side: 2.364706479 Break this problem into two subproblems by setting (x + 1.857142857) equal to 2.364706479 and -2.364706479.Subproblem 1
x + 1.857142857 = 2.364706479 Simplifying x + 1.857142857 = 2.364706479 Reorder the terms: 1.857142857 + x = 2.364706479 Solving 1.857142857 + x = 2.364706479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + x = 2.364706479 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + x = 2.364706479 + -1.857142857 x = 2.364706479 + -1.857142857 Combine like terms: 2.364706479 + -1.857142857 = 0.507563622 x = 0.507563622 Simplifying x = 0.507563622Subproblem 2
x + 1.857142857 = -2.364706479 Simplifying x + 1.857142857 = -2.364706479 Reorder the terms: 1.857142857 + x = -2.364706479 Solving 1.857142857 + x = -2.364706479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + x = -2.364706479 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + x = -2.364706479 + -1.857142857 x = -2.364706479 + -1.857142857 Combine like terms: -2.364706479 + -1.857142857 = -4.221849336 x = -4.221849336 Simplifying x = -4.221849336Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.507563622, -4.221849336}
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