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Simplifying 163.1(4 + 6x) = [4x + 3x2] (4 * 163.1 + 6x * 163.1) = [4x + 3x2] (652.4 + 978.6x) = [4x + 3x2] Remove brackets around [4x + 3x2] 652.4 + 978.6x = 4x + 3x2 Solving 652.4 + 978.6x = 4x + 3x2 Solving for variable 'x'. Combine like terms: 978.6x + -4x = 974.6x 652.4 + 974.6x + -3x2 = 4x + 3x2 + -4x + -3x2 Reorder the terms: 652.4 + 974.6x + -3x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 652.4 + 974.6x + -3x2 = 0 + 3x2 + -3x2 652.4 + 974.6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 652.4 + 974.6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -217.4666667 + -324.8666667x + x2 = 0 Move the constant term to the right: Add '217.4666667' to each side of the equation. -217.4666667 + -324.8666667x + 217.4666667 + x2 = 0 + 217.4666667 Reorder the terms: -217.4666667 + 217.4666667 + -324.8666667x + x2 = 0 + 217.4666667 Combine like terms: -217.4666667 + 217.4666667 = 0.0000000 0.0000000 + -324.8666667x + x2 = 0 + 217.4666667 -324.8666667x + x2 = 0 + 217.4666667 Combine like terms: 0 + 217.4666667 = 217.4666667 -324.8666667x + x2 = 217.4666667 The x term is -324.8666667x. Take half its coefficient (-162.4333334). Square it (26384.58780) and add it to both sides. Add '26384.58780' to each side of the equation. -324.8666667x + 26384.58780 + x2 = 217.4666667 + 26384.58780 Reorder the terms: 26384.58780 + -324.8666667x + x2 = 217.4666667 + 26384.58780 Combine like terms: 217.4666667 + 26384.58780 = 26602.0544667 26384.58780 + -324.8666667x + x2 = 26602.0544667 Factor a perfect square on the left side: (x + -162.4333334)(x + -162.4333334) = 26602.0544667 Calculate the square root of the right side: 163.101362553 Break this problem into two subproblems by setting (x + -162.4333334) equal to 163.101362553 and -163.101362553.Subproblem 1
x + -162.4333334 = 163.101362553 Simplifying x + -162.4333334 = 163.101362553 Reorder the terms: -162.4333334 + x = 163.101362553 Solving -162.4333334 + x = 163.101362553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '162.4333334' to each side of the equation. -162.4333334 + 162.4333334 + x = 163.101362553 + 162.4333334 Combine like terms: -162.4333334 + 162.4333334 = 0.0000000 0.0000000 + x = 163.101362553 + 162.4333334 x = 163.101362553 + 162.4333334 Combine like terms: 163.101362553 + 162.4333334 = 325.534695953 x = 325.534695953 Simplifying x = 325.534695953Subproblem 2
x + -162.4333334 = -163.101362553 Simplifying x + -162.4333334 = -163.101362553 Reorder the terms: -162.4333334 + x = -163.101362553 Solving -162.4333334 + x = -163.101362553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '162.4333334' to each side of the equation. -162.4333334 + 162.4333334 + x = -163.101362553 + 162.4333334 Combine like terms: -162.4333334 + 162.4333334 = 0.0000000 0.0000000 + x = -163.101362553 + 162.4333334 x = -163.101362553 + 162.4333334 Combine like terms: -163.101362553 + 162.4333334 = -0.668029153 x = -0.668029153 Simplifying x = -0.668029153Solution
The solution to the problem is based on the solutions from the subproblems. x = {325.534695953, -0.668029153}
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