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Simplifying 4x(x * 10) = -7x + 65 Reorder the terms for easier multiplication: 4x(10x) = -7x + 65 Remove parenthesis around (10x) 4x * 10x = -7x + 65 Reorder the terms for easier multiplication: 4 * 10x * x = -7x + 65 Multiply 4 * 10 40x * x = -7x + 65 Multiply x * x 40x2 = -7x + 65 Reorder the terms: 40x2 = 65 + -7x Solving 40x2 = 65 + -7x Solving for variable 'x'. Reorder the terms: -65 + 7x + 40x2 = 65 + -7x + -65 + 7x Reorder the terms: -65 + 7x + 40x2 = 65 + -65 + -7x + 7x Combine like terms: 65 + -65 = 0 -65 + 7x + 40x2 = 0 + -7x + 7x -65 + 7x + 40x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -65 + 7x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -1.625 + 0.175x + x2 = 0.0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 0.175x + 1.625 + x2 = 0.0 + 1.625 Reorder the terms: -1.625 + 1.625 + 0.175x + x2 = 0.0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 0.175x + x2 = 0.0 + 1.625 0.175x + x2 = 0.0 + 1.625 Combine like terms: 0.0 + 1.625 = 1.625 0.175x + x2 = 1.625 The x term is 0.175x. Take half its coefficient (0.0875). Square it (0.00765625) and add it to both sides. Add '0.00765625' to each side of the equation. 0.175x + 0.00765625 + x2 = 1.625 + 0.00765625 Reorder the terms: 0.00765625 + 0.175x + x2 = 1.625 + 0.00765625 Combine like terms: 1.625 + 0.00765625 = 1.63265625 0.00765625 + 0.175x + x2 = 1.63265625 Factor a perfect square on the left side: (x + 0.0875)(x + 0.0875) = 1.63265625 Calculate the square root of the right side: 1.277754378 Break this problem into two subproblems by setting (x + 0.0875) equal to 1.277754378 and -1.277754378.Subproblem 1
x + 0.0875 = 1.277754378 Simplifying x + 0.0875 = 1.277754378 Reorder the terms: 0.0875 + x = 1.277754378 Solving 0.0875 + x = 1.277754378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0875' to each side of the equation. 0.0875 + -0.0875 + x = 1.277754378 + -0.0875 Combine like terms: 0.0875 + -0.0875 = 0.0000 0.0000 + x = 1.277754378 + -0.0875 x = 1.277754378 + -0.0875 Combine like terms: 1.277754378 + -0.0875 = 1.190254378 x = 1.190254378 Simplifying x = 1.190254378Subproblem 2
x + 0.0875 = -1.277754378 Simplifying x + 0.0875 = -1.277754378 Reorder the terms: 0.0875 + x = -1.277754378 Solving 0.0875 + x = -1.277754378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0875' to each side of the equation. 0.0875 + -0.0875 + x = -1.277754378 + -0.0875 Combine like terms: 0.0875 + -0.0875 = 0.0000 0.0000 + x = -1.277754378 + -0.0875 x = -1.277754378 + -0.0875 Combine like terms: -1.277754378 + -0.0875 = -1.365254378 x = -1.365254378 Simplifying x = -1.365254378Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.190254378, -1.365254378}
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