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Simplifying 4x * -5x + 7 = 7x + 2 Reorder the terms for easier multiplication: 4 * -5x * x + 7 = 7x + 2 Multiply 4 * -5 -20x * x + 7 = 7x + 2 Multiply x * x -20x2 + 7 = 7x + 2 Reorder the terms: 7 + -20x2 = 7x + 2 Reorder the terms: 7 + -20x2 = 2 + 7x Solving 7 + -20x2 = 2 + 7x Solving for variable 'x'. Reorder the terms: 7 + -2 + -7x + -20x2 = 2 + 7x + -2 + -7x Combine like terms: 7 + -2 = 5 5 + -7x + -20x2 = 2 + 7x + -2 + -7x Reorder the terms: 5 + -7x + -20x2 = 2 + -2 + 7x + -7x Combine like terms: 2 + -2 = 0 5 + -7x + -20x2 = 0 + 7x + -7x 5 + -7x + -20x2 = 7x + -7x Combine like terms: 7x + -7x = 0 5 + -7x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.25 + 0.35x + x2 = 0.0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.35x + 0.25 + x2 = 0.0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.35x + x2 = 0.0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.35x + x2 = 0.0 + 0.25 0.35x + x2 = 0.0 + 0.25 Combine like terms: 0.0 + 0.25 = 0.25 0.35x + x2 = 0.25 The x term is 0.35x. Take half its coefficient (0.175). Square it (0.030625) and add it to both sides. Add '0.030625' to each side of the equation. 0.35x + 0.030625 + x2 = 0.25 + 0.030625 Reorder the terms: 0.030625 + 0.35x + x2 = 0.25 + 0.030625 Combine like terms: 0.25 + 0.030625 = 0.280625 0.030625 + 0.35x + x2 = 0.280625 Factor a perfect square on the left side: (x + 0.175)(x + 0.175) = 0.280625 Calculate the square root of the right side: 0.529740503 Break this problem into two subproblems by setting (x + 0.175) equal to 0.529740503 and -0.529740503.Subproblem 1
x + 0.175 = 0.529740503 Simplifying x + 0.175 = 0.529740503 Reorder the terms: 0.175 + x = 0.529740503 Solving 0.175 + x = 0.529740503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = 0.529740503 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = 0.529740503 + -0.175 x = 0.529740503 + -0.175 Combine like terms: 0.529740503 + -0.175 = 0.354740503 x = 0.354740503 Simplifying x = 0.354740503Subproblem 2
x + 0.175 = -0.529740503 Simplifying x + 0.175 = -0.529740503 Reorder the terms: 0.175 + x = -0.529740503 Solving 0.175 + x = -0.529740503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = -0.529740503 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = -0.529740503 + -0.175 x = -0.529740503 + -0.175 Combine like terms: -0.529740503 + -0.175 = -0.704740503 x = -0.704740503 Simplifying x = -0.704740503Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.354740503, -0.704740503}
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