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Simplifying 4(3x + 2)(4x + -5) + -7x = 0 Reorder the terms: 4(2 + 3x)(4x + -5) + -7x = 0 Reorder the terms: 4(2 + 3x)(-5 + 4x) + -7x = 0 Multiply (2 + 3x) * (-5 + 4x) 4(2(-5 + 4x) + 3x * (-5 + 4x)) + -7x = 0 4((-5 * 2 + 4x * 2) + 3x * (-5 + 4x)) + -7x = 0 4((-10 + 8x) + 3x * (-5 + 4x)) + -7x = 0 4(-10 + 8x + (-5 * 3x + 4x * 3x)) + -7x = 0 4(-10 + 8x + (-15x + 12x2)) + -7x = 0 Combine like terms: 8x + -15x = -7x 4(-10 + -7x + 12x2) + -7x = 0 (-10 * 4 + -7x * 4 + 12x2 * 4) + -7x = 0 (-40 + -28x + 48x2) + -7x = 0 Reorder the terms: -40 + -28x + -7x + 48x2 = 0 Combine like terms: -28x + -7x = -35x -40 + -35x + 48x2 = 0 Solving -40 + -35x + 48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.8333333333 + -0.7291666667x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -0.7291666667x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -0.7291666667x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -0.7291666667x + x2 = 0 + 0.8333333333 -0.7291666667x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -0.7291666667x + x2 = 0.8333333333 The x term is -0.7291666667x. Take half its coefficient (-0.3645833334). Square it (0.1329210070) and add it to both sides. Add '0.1329210070' to each side of the equation. -0.7291666667x + 0.1329210070 + x2 = 0.8333333333 + 0.1329210070 Reorder the terms: 0.1329210070 + -0.7291666667x + x2 = 0.8333333333 + 0.1329210070 Combine like terms: 0.8333333333 + 0.1329210070 = 0.9662543403 0.1329210070 + -0.7291666667x + x2 = 0.9662543403 Factor a perfect square on the left side: (x + -0.3645833334)(x + -0.3645833334) = 0.9662543403 Calculate the square root of the right side: 0.98298237 Break this problem into two subproblems by setting (x + -0.3645833334) equal to 0.98298237 and -0.98298237.Subproblem 1
x + -0.3645833334 = 0.98298237 Simplifying x + -0.3645833334 = 0.98298237 Reorder the terms: -0.3645833334 + x = 0.98298237 Solving -0.3645833334 + x = 0.98298237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3645833334' to each side of the equation. -0.3645833334 + 0.3645833334 + x = 0.98298237 + 0.3645833334 Combine like terms: -0.3645833334 + 0.3645833334 = 0.0000000000 0.0000000000 + x = 0.98298237 + 0.3645833334 x = 0.98298237 + 0.3645833334 Combine like terms: 0.98298237 + 0.3645833334 = 1.3475657034 x = 1.3475657034 Simplifying x = 1.3475657034Subproblem 2
x + -0.3645833334 = -0.98298237 Simplifying x + -0.3645833334 = -0.98298237 Reorder the terms: -0.3645833334 + x = -0.98298237 Solving -0.3645833334 + x = -0.98298237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3645833334' to each side of the equation. -0.3645833334 + 0.3645833334 + x = -0.98298237 + 0.3645833334 Combine like terms: -0.3645833334 + 0.3645833334 = 0.0000000000 0.0000000000 + x = -0.98298237 + 0.3645833334 x = -0.98298237 + 0.3645833334 Combine like terms: -0.98298237 + 0.3645833334 = -0.6183990366 x = -0.6183990366 Simplifying x = -0.6183990366Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3475657034, -0.6183990366}
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