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Simplifying 3x(10 + -1x) = 21 (10 * 3x + -1x * 3x) = 21 (30x + -3x2) = 21 Solving 30x + -3x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 30x + -3x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 30x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 10x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying -7 + 10x + -1x2 = 0 Solving -7 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -10x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -10x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -10x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -10x + x2 = 0 + -7 -10x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -10x + x2 = -7 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -7 + 25 Reorder the terms: 25 + -10x + x2 = -7 + 25 Combine like terms: -7 + 25 = 18 25 + -10x + x2 = 18 Factor a perfect square on the left side: (x + -5)(x + -5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -5) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -5 = 4.242640687 Simplifying x + -5 = 4.242640687 Reorder the terms: -5 + x = 4.242640687 Solving -5 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.242640687 + 5 x = 4.242640687 + 5 Combine like terms: 4.242640687 + 5 = 9.242640687 x = 9.242640687 Simplifying x = 9.242640687Subproblem 2
x + -5 = -4.242640687 Simplifying x + -5 = -4.242640687 Reorder the terms: -5 + x = -4.242640687 Solving -5 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.242640687 + 5 x = -4.242640687 + 5 Combine like terms: -4.242640687 + 5 = 0.757359313 x = 0.757359313 Simplifying x = 0.757359313Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.242640687, 0.757359313}Solution
x = {9.242640687, 0.757359313}
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