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Simplifying 7x2 + -14x = 100 Reorder the terms: -14x + 7x2 = 100 Solving -14x + 7x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + -14x + 7x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -14.28571429 + -2x + x2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + -2x + 14.28571429 + x2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + -2x + x2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + -2x + x2 = 0 + 14.28571429 -2x + x2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 -2x + x2 = 14.28571429 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 14.28571429 + 1 Reorder the terms: 1 + -2x + x2 = 14.28571429 + 1 Combine like terms: 14.28571429 + 1 = 15.28571429 1 + -2x + x2 = 15.28571429 Factor a perfect square on the left side: (x + -1)(x + -1) = 15.28571429 Calculate the square root of the right side: 3.90969491 Break this problem into two subproblems by setting (x + -1) equal to 3.90969491 and -3.90969491.Subproblem 1
x + -1 = 3.90969491 Simplifying x + -1 = 3.90969491 Reorder the terms: -1 + x = 3.90969491 Solving -1 + x = 3.90969491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.90969491 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.90969491 + 1 x = 3.90969491 + 1 Combine like terms: 3.90969491 + 1 = 4.90969491 x = 4.90969491 Simplifying x = 4.90969491Subproblem 2
x + -1 = -3.90969491 Simplifying x + -1 = -3.90969491 Reorder the terms: -1 + x = -3.90969491 Solving -1 + x = -3.90969491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.90969491 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.90969491 + 1 x = -3.90969491 + 1 Combine like terms: -3.90969491 + 1 = -2.90969491 x = -2.90969491 Simplifying x = -2.90969491Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.90969491, -2.90969491}
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