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Simplifying 5(x + -5) * 7x + 4 = 0 Reorder the terms: 5(-5 + x) * 7x + 4 = 0 Reorder the terms for easier multiplication: 5 * 7x(-5 + x) + 4 = 0 Multiply 5 * 7 35x(-5 + x) + 4 = 0 (-5 * 35x + x * 35x) + 4 = 0 (-175x + 35x2) + 4 = 0 Reorder the terms: 4 + -175x + 35x2 = 0 Solving 4 + -175x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.1142857143 + -5x + x2 = 0 Move the constant term to the right: Add '-0.1142857143' to each side of the equation. 0.1142857143 + -5x + -0.1142857143 + x2 = 0 + -0.1142857143 Reorder the terms: 0.1142857143 + -0.1142857143 + -5x + x2 = 0 + -0.1142857143 Combine like terms: 0.1142857143 + -0.1142857143 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + -0.1142857143 -5x + x2 = 0 + -0.1142857143 Combine like terms: 0 + -0.1142857143 = -0.1142857143 -5x + x2 = -0.1142857143 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.1142857143 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.1142857143 + 6.25 Combine like terms: -0.1142857143 + 6.25 = 6.1357142857 6.25 + -5x + x2 = 6.1357142857 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.1357142857 Calculate the square root of the right side: 2.477037401 Break this problem into two subproblems by setting (x + -2.5) equal to 2.477037401 and -2.477037401.Subproblem 1
x + -2.5 = 2.477037401 Simplifying x + -2.5 = 2.477037401 Reorder the terms: -2.5 + x = 2.477037401 Solving -2.5 + x = 2.477037401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.477037401 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.477037401 + 2.5 x = 2.477037401 + 2.5 Combine like terms: 2.477037401 + 2.5 = 4.977037401 x = 4.977037401 Simplifying x = 4.977037401Subproblem 2
x + -2.5 = -2.477037401 Simplifying x + -2.5 = -2.477037401 Reorder the terms: -2.5 + x = -2.477037401 Solving -2.5 + x = -2.477037401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.477037401 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.477037401 + 2.5 x = -2.477037401 + 2.5 Combine like terms: -2.477037401 + 2.5 = 0.022962599 x = 0.022962599 Simplifying x = 0.022962599Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.977037401, 0.022962599}
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