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Simplifying -2x2 + 14x + -21 = 0 Reorder the terms: -21 + 14x + -2x2 = 0 Solving -21 + 14x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 10.5 + -7x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -7x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -7x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -7x + x2 = 0 + -10.5 -7x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -7x + x2 = -10.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -10.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -10.5 + 12.25 Combine like terms: -10.5 + 12.25 = 1.75 12.25 + -7x + x2 = 1.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -3.5) equal to 1.322875656 and -1.322875656.Subproblem 1
x + -3.5 = 1.322875656 Simplifying x + -3.5 = 1.322875656 Reorder the terms: -3.5 + x = 1.322875656 Solving -3.5 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.322875656 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.322875656 + 3.5 x = 1.322875656 + 3.5 Combine like terms: 1.322875656 + 3.5 = 4.822875656 x = 4.822875656 Simplifying x = 4.822875656Subproblem 2
x + -3.5 = -1.322875656 Simplifying x + -3.5 = -1.322875656 Reorder the terms: -3.5 + x = -1.322875656 Solving -3.5 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.322875656 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.322875656 + 3.5 x = -1.322875656 + 3.5 Combine like terms: -1.322875656 + 3.5 = 2.177124344 x = 2.177124344 Simplifying x = 2.177124344Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.822875656, 2.177124344}
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