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Simplifying 4(3x + 7) * 6x + -5 = 0 Reorder the terms: 4(7 + 3x) * 6x + -5 = 0 Reorder the terms for easier multiplication: 4 * 6x(7 + 3x) + -5 = 0 Multiply 4 * 6 24x(7 + 3x) + -5 = 0 (7 * 24x + 3x * 24x) + -5 = 0 (168x + 72x2) + -5 = 0 Reorder the terms: -5 + 168x + 72x2 = 0 Solving -5 + 168x + 72x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. -0.06944444444 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '0.06944444444' to each side of the equation. -0.06944444444 + 2.333333333x + 0.06944444444 + x2 = 0 + 0.06944444444 Reorder the terms: -0.06944444444 + 0.06944444444 + 2.333333333x + x2 = 0 + 0.06944444444 Combine like terms: -0.06944444444 + 0.06944444444 = 0.00000000000 0.00000000000 + 2.333333333x + x2 = 0 + 0.06944444444 2.333333333x + x2 = 0 + 0.06944444444 Combine like terms: 0 + 0.06944444444 = 0.06944444444 2.333333333x + x2 = 0.06944444444 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 0.06944444444 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 0.06944444444 + 1.361111112 Combine like terms: 0.06944444444 + 1.361111112 = 1.43055555644 1.361111112 + 2.333333333x + x2 = 1.43055555644 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 1.43055555644 Calculate the square root of the right side: 1.196058342 Break this problem into two subproblems by setting (x + 1.166666667) equal to 1.196058342 and -1.196058342.Subproblem 1
x + 1.166666667 = 1.196058342 Simplifying x + 1.166666667 = 1.196058342 Reorder the terms: 1.166666667 + x = 1.196058342 Solving 1.166666667 + x = 1.196058342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 1.196058342 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 1.196058342 + -1.166666667 x = 1.196058342 + -1.166666667 Combine like terms: 1.196058342 + -1.166666667 = 0.029391675 x = 0.029391675 Simplifying x = 0.029391675Subproblem 2
x + 1.166666667 = -1.196058342 Simplifying x + 1.166666667 = -1.196058342 Reorder the terms: 1.166666667 + x = -1.196058342 Solving 1.166666667 + x = -1.196058342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -1.196058342 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -1.196058342 + -1.166666667 x = -1.196058342 + -1.166666667 Combine like terms: -1.196058342 + -1.166666667 = -2.362725009 x = -2.362725009 Simplifying x = -2.362725009Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.029391675, -2.362725009}
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