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Simplifying 3x(4x) + 7x(5x) = 2x + 5 Remove parenthesis around (4x) 3x * 4x + 7x(5x) = 2x + 5 Reorder the terms for easier multiplication: 3 * 4x * x + 7x(5x) = 2x + 5 Multiply 3 * 4 12x * x + 7x(5x) = 2x + 5 Multiply x * x 12x2 + 7x(5x) = 2x + 5 Remove parenthesis around (5x) 12x2 + 7x * 5x = 2x + 5 Reorder the terms for easier multiplication: 12x2 + 7 * 5x * x = 2x + 5 Multiply 7 * 5 12x2 + 35x * x = 2x + 5 Multiply x * x 12x2 + 35x2 = 2x + 5 Combine like terms: 12x2 + 35x2 = 47x2 47x2 = 2x + 5 Reorder the terms: 47x2 = 5 + 2x Solving 47x2 = 5 + 2x Solving for variable 'x'. Reorder the terms: -5 + -2x + 47x2 = 5 + 2x + -5 + -2x Reorder the terms: -5 + -2x + 47x2 = 5 + -5 + 2x + -2x Combine like terms: 5 + -5 = 0 -5 + -2x + 47x2 = 0 + 2x + -2x -5 + -2x + 47x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -5 + -2x + 47x2 = 0 Begin completing the square. Divide all terms by 47 the coefficient of the squared term: Divide each side by '47'. -0.1063829787 + -0.04255319149x + x2 = 0 Move the constant term to the right: Add '0.1063829787' to each side of the equation. -0.1063829787 + -0.04255319149x + 0.1063829787 + x2 = 0 + 0.1063829787 Reorder the terms: -0.1063829787 + 0.1063829787 + -0.04255319149x + x2 = 0 + 0.1063829787 Combine like terms: -0.1063829787 + 0.1063829787 = 0.0000000000 0.0000000000 + -0.04255319149x + x2 = 0 + 0.1063829787 -0.04255319149x + x2 = 0 + 0.1063829787 Combine like terms: 0 + 0.1063829787 = 0.1063829787 -0.04255319149x + x2 = 0.1063829787 The x term is -0.04255319149x. Take half its coefficient (-0.02127659575). Square it (0.0004526935267) and add it to both sides. Add '0.0004526935267' to each side of the equation. -0.04255319149x + 0.0004526935267 + x2 = 0.1063829787 + 0.0004526935267 Reorder the terms: 0.0004526935267 + -0.04255319149x + x2 = 0.1063829787 + 0.0004526935267 Combine like terms: 0.1063829787 + 0.0004526935267 = 0.1068356722267 0.0004526935267 + -0.04255319149x + x2 = 0.1068356722267 Factor a perfect square on the left side: (x + -0.02127659575)(x + -0.02127659575) = 0.1068356722267 Calculate the square root of the right side: 0.326857266 Break this problem into two subproblems by setting (x + -0.02127659575) equal to 0.326857266 and -0.326857266.Subproblem 1
x + -0.02127659575 = 0.326857266 Simplifying x + -0.02127659575 = 0.326857266 Reorder the terms: -0.02127659575 + x = 0.326857266 Solving -0.02127659575 + x = 0.326857266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02127659575' to each side of the equation. -0.02127659575 + 0.02127659575 + x = 0.326857266 + 0.02127659575 Combine like terms: -0.02127659575 + 0.02127659575 = 0.00000000000 0.00000000000 + x = 0.326857266 + 0.02127659575 x = 0.326857266 + 0.02127659575 Combine like terms: 0.326857266 + 0.02127659575 = 0.34813386175 x = 0.34813386175 Simplifying x = 0.34813386175Subproblem 2
x + -0.02127659575 = -0.326857266 Simplifying x + -0.02127659575 = -0.326857266 Reorder the terms: -0.02127659575 + x = -0.326857266 Solving -0.02127659575 + x = -0.326857266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02127659575' to each side of the equation. -0.02127659575 + 0.02127659575 + x = -0.326857266 + 0.02127659575 Combine like terms: -0.02127659575 + 0.02127659575 = 0.00000000000 0.00000000000 + x = -0.326857266 + 0.02127659575 x = -0.326857266 + 0.02127659575 Combine like terms: -0.326857266 + 0.02127659575 = -0.30558067025 x = -0.30558067025 Simplifying x = -0.30558067025Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34813386175, -0.30558067025}
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