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Simplifying 4[3(7x + -1)(3x + 4)] = 5x + -47 Reorder the terms: 4[3(-1 + 7x)(3x + 4)] = 5x + -47 Reorder the terms: 4[3(-1 + 7x)(4 + 3x)] = 5x + -47 Multiply (-1 + 7x) * (4 + 3x) 4[3(-1(4 + 3x) + 7x * (4 + 3x))] = 5x + -47 4[3((4 * -1 + 3x * -1) + 7x * (4 + 3x))] = 5x + -47 4[3((-4 + -3x) + 7x * (4 + 3x))] = 5x + -47 4[3(-4 + -3x + (4 * 7x + 3x * 7x))] = 5x + -47 4[3(-4 + -3x + (28x + 21x2))] = 5x + -47 Combine like terms: -3x + 28x = 25x 4[3(-4 + 25x + 21x2)] = 5x + -47 4[(-4 * 3 + 25x * 3 + 21x2 * 3)] = 5x + -47 4[(-12 + 75x + 63x2)] = 5x + -47 [-12 * 4 + 75x * 4 + 63x2 * 4] = 5x + -47 [-48 + 300x + 252x2] = 5x + -47 Reorder the terms: -48 + 300x + 252x2 = -47 + 5x Solving -48 + 300x + 252x2 = -47 + 5x Solving for variable 'x'. Reorder the terms: -48 + 47 + 300x + -5x + 252x2 = -47 + 5x + 47 + -5x Combine like terms: -48 + 47 = -1 -1 + 300x + -5x + 252x2 = -47 + 5x + 47 + -5x Combine like terms: 300x + -5x = 295x -1 + 295x + 252x2 = -47 + 5x + 47 + -5x Reorder the terms: -1 + 295x + 252x2 = -47 + 47 + 5x + -5x Combine like terms: -47 + 47 = 0 -1 + 295x + 252x2 = 0 + 5x + -5x -1 + 295x + 252x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -1 + 295x + 252x2 = 0 Begin completing the square. Divide all terms by 252 the coefficient of the squared term: Divide each side by '252'. -0.003968253968 + 1.170634921x + x2 = 0 Move the constant term to the right: Add '0.003968253968' to each side of the equation. -0.003968253968 + 1.170634921x + 0.003968253968 + x2 = 0 + 0.003968253968 Reorder the terms: -0.003968253968 + 0.003968253968 + 1.170634921x + x2 = 0 + 0.003968253968 Combine like terms: -0.003968253968 + 0.003968253968 = 0.000000000000 0.000000000000 + 1.170634921x + x2 = 0 + 0.003968253968 1.170634921x + x2 = 0 + 0.003968253968 Combine like terms: 0 + 0.003968253968 = 0.003968253968 1.170634921x + x2 = 0.003968253968 The x term is 1.170634921x. Take half its coefficient (0.5853174605). Square it (0.3425965296) and add it to both sides. Add '0.3425965296' to each side of the equation. 1.170634921x + 0.3425965296 + x2 = 0.003968253968 + 0.3425965296 Reorder the terms: 0.3425965296 + 1.170634921x + x2 = 0.003968253968 + 0.3425965296 Combine like terms: 0.003968253968 + 0.3425965296 = 0.346564783568 0.3425965296 + 1.170634921x + x2 = 0.346564783568 Factor a perfect square on the left side: (x + 0.5853174605)(x + 0.5853174605) = 0.346564783568 Calculate the square root of the right side: 0.588697531 Break this problem into two subproblems by setting (x + 0.5853174605) equal to 0.588697531 and -0.588697531.Subproblem 1
x + 0.5853174605 = 0.588697531 Simplifying x + 0.5853174605 = 0.588697531 Reorder the terms: 0.5853174605 + x = 0.588697531 Solving 0.5853174605 + x = 0.588697531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5853174605' to each side of the equation. 0.5853174605 + -0.5853174605 + x = 0.588697531 + -0.5853174605 Combine like terms: 0.5853174605 + -0.5853174605 = 0.0000000000 0.0000000000 + x = 0.588697531 + -0.5853174605 x = 0.588697531 + -0.5853174605 Combine like terms: 0.588697531 + -0.5853174605 = 0.0033800705 x = 0.0033800705 Simplifying x = 0.0033800705Subproblem 2
x + 0.5853174605 = -0.588697531 Simplifying x + 0.5853174605 = -0.588697531 Reorder the terms: 0.5853174605 + x = -0.588697531 Solving 0.5853174605 + x = -0.588697531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5853174605' to each side of the equation. 0.5853174605 + -0.5853174605 + x = -0.588697531 + -0.5853174605 Combine like terms: 0.5853174605 + -0.5853174605 = 0.0000000000 0.0000000000 + x = -0.588697531 + -0.5853174605 x = -0.588697531 + -0.5853174605 Combine like terms: -0.588697531 + -0.5853174605 = -1.1740149915 x = -1.1740149915 Simplifying x = -1.1740149915Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0033800705, -1.1740149915}
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