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Simplifying -5x2 + 14x + -7 = 0 Reorder the terms: -7 + 14x + -5x2 = 0 Solving -7 + 14x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.4 + -2.8x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -2.8x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -2.8x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -2.8x + x2 = 0 + -1.4 -2.8x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -2.8x + x2 = -1.4 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = -1.4 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = -1.4 + 1.96 Combine like terms: -1.4 + 1.96 = 0.56 1.96 + -2.8x + x2 = 0.56 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (x + -1.4) equal to 0.748331477 and -0.748331477.Subproblem 1
x + -1.4 = 0.748331477 Simplifying x + -1.4 = 0.748331477 Reorder the terms: -1.4 + x = 0.748331477 Solving -1.4 + x = 0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 0.748331477 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 0.748331477 + 1.4 x = 0.748331477 + 1.4 Combine like terms: 0.748331477 + 1.4 = 2.148331477 x = 2.148331477 Simplifying x = 2.148331477Subproblem 2
x + -1.4 = -0.748331477 Simplifying x + -1.4 = -0.748331477 Reorder the terms: -1.4 + x = -0.748331477 Solving -1.4 + x = -0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -0.748331477 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -0.748331477 + 1.4 x = -0.748331477 + 1.4 Combine like terms: -0.748331477 + 1.4 = 0.651668523 x = 0.651668523 Simplifying x = 0.651668523Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.148331477, 0.651668523}
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