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Simplifying 3x2 + 10x = 21 Reorder the terms: 10x + 3x2 = 21 Solving 10x + 3x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 10x + 3x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 3.333333333x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 3.333333333x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3.333333333x + x2 = 0 + 7 3.333333333x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 3.333333333x + x2 = 7 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 7 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 7 + 2.777777779 Combine like terms: 7 + 2.777777779 = 9.777777779 2.777777779 + 3.333333333x + x2 = 9.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 9.777777779 Calculate the square root of the right side: 3.12694384 Break this problem into two subproblems by setting (x + 1.666666667) equal to 3.12694384 and -3.12694384.Subproblem 1
x + 1.666666667 = 3.12694384 Simplifying x + 1.666666667 = 3.12694384 Reorder the terms: 1.666666667 + x = 3.12694384 Solving 1.666666667 + x = 3.12694384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 3.12694384 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 3.12694384 + -1.666666667 x = 3.12694384 + -1.666666667 Combine like terms: 3.12694384 + -1.666666667 = 1.460277173 x = 1.460277173 Simplifying x = 1.460277173Subproblem 2
x + 1.666666667 = -3.12694384 Simplifying x + 1.666666667 = -3.12694384 Reorder the terms: 1.666666667 + x = -3.12694384 Solving 1.666666667 + x = -3.12694384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -3.12694384 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -3.12694384 + -1.666666667 x = -3.12694384 + -1.666666667 Combine like terms: -3.12694384 + -1.666666667 = -4.793610507 x = -4.793610507 Simplifying x = -4.793610507Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.460277173, -4.793610507}
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