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Simplifying 32x2 + 48x + -7 = 0 Reorder the terms: -7 + 48x + 32x2 = 0 Solving -7 + 48x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.21875 + 1.5x + x2 = 0 Move the constant term to the right: Add '0.21875' to each side of the equation. -0.21875 + 1.5x + 0.21875 + x2 = 0 + 0.21875 Reorder the terms: -0.21875 + 0.21875 + 1.5x + x2 = 0 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + 1.5x + x2 = 0 + 0.21875 1.5x + x2 = 0 + 0.21875 Combine like terms: 0 + 0.21875 = 0.21875 1.5x + x2 = 0.21875 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 0.21875 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.21875 + 0.5625 Combine like terms: 0.21875 + 0.5625 = 0.78125 0.5625 + 1.5x + x2 = 0.78125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.78125 Calculate the square root of the right side: 0.883883476 Break this problem into two subproblems by setting (x + 0.75) equal to 0.883883476 and -0.883883476.Subproblem 1
x + 0.75 = 0.883883476 Simplifying x + 0.75 = 0.883883476 Reorder the terms: 0.75 + x = 0.883883476 Solving 0.75 + x = 0.883883476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.883883476 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.883883476 + -0.75 x = 0.883883476 + -0.75 Combine like terms: 0.883883476 + -0.75 = 0.133883476 x = 0.133883476 Simplifying x = 0.133883476Subproblem 2
x + 0.75 = -0.883883476 Simplifying x + 0.75 = -0.883883476 Reorder the terms: 0.75 + x = -0.883883476 Solving 0.75 + x = -0.883883476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -0.883883476 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.883883476 + -0.75 x = -0.883883476 + -0.75 Combine like terms: -0.883883476 + -0.75 = -1.633883476 x = -1.633883476 Simplifying x = -1.633883476Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.133883476, -1.633883476}
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