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Simplifying -7x2 + 28x + -25 = 0 Reorder the terms: -25 + 28x + -7x2 = 0 Solving -25 + 28x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 3.571428571 + -4x + x2 = 0 Move the constant term to the right: Add '-3.571428571' to each side of the equation. 3.571428571 + -4x + -3.571428571 + x2 = 0 + -3.571428571 Reorder the terms: 3.571428571 + -3.571428571 + -4x + x2 = 0 + -3.571428571 Combine like terms: 3.571428571 + -3.571428571 = 0.000000000 0.000000000 + -4x + x2 = 0 + -3.571428571 -4x + x2 = 0 + -3.571428571 Combine like terms: 0 + -3.571428571 = -3.571428571 -4x + x2 = -3.571428571 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.571428571 + 4 Reorder the terms: 4 + -4x + x2 = -3.571428571 + 4 Combine like terms: -3.571428571 + 4 = 0.428571429 4 + -4x + x2 = 0.428571429 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.428571429 Calculate the square root of the right side: 0.654653671 Break this problem into two subproblems by setting (x + -2) equal to 0.654653671 and -0.654653671.Subproblem 1
x + -2 = 0.654653671 Simplifying x + -2 = 0.654653671 Reorder the terms: -2 + x = 0.654653671 Solving -2 + x = 0.654653671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.654653671 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.654653671 + 2 x = 0.654653671 + 2 Combine like terms: 0.654653671 + 2 = 2.654653671 x = 2.654653671 Simplifying x = 2.654653671Subproblem 2
x + -2 = -0.654653671 Simplifying x + -2 = -0.654653671 Reorder the terms: -2 + x = -0.654653671 Solving -2 + x = -0.654653671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.654653671 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.654653671 + 2 x = -0.654653671 + 2 Combine like terms: -0.654653671 + 2 = 1.345346329 x = 1.345346329 Simplifying x = 1.345346329Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.654653671, 1.345346329}
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